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Journal articles on the topic 'Primitive elements'

Author: Grafiati

Published: 25 May 2024

Last updated: 31 July 2025

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1

Konieczny, Jochen, Gerhard Rosenberger, and Julia Wolny. "Tame Almost Primitive Elements." Results in Mathematics 38, no. 1-2 (2000): 116–29. http://dx.doi.org/10.1007/bf03322435.

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2

Artamonov, V. A., A. V. Klimakov, A. A. Mikhalev, and A. V. Mikhalev. "Primitive and Almost Primitive Elements of Schreier Varieties." Journal of Mathematical Sciences 237, no. 2 (2019): 157–79. http://dx.doi.org/10.1007/s10958-019-4148-2.

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3

de Smit, Bart. "Primitive elements in integral bases." Acta Arithmetica 71, no. 2 (1995): 159–70. http://dx.doi.org/10.4064/aa-71-2-159-170.

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4

Booker, Andrew R., Stephen D. Cohen, Nicol Leong, and Tim Trudgian. "Primitive elements with prescribed traces." Finite Fields and Their Applications 84 (December 2022): 102094. http://dx.doi.org/10.1016/j.ffa.2022.102094.

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5

Evans, Martin J. "Primitive elements in free groups." Proceedings of the American Mathematical Society 106, no. 2 (1989): 313. http://dx.doi.org/10.1090/s0002-9939-1989-0952315-1.

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6

Umirbaev, U. U. "Primitive elements of free groups." Russian Mathematical Surveys 49, no. 2 (1994): 184–85. http://dx.doi.org/10.1070/rm1994v049n02abeh002233.

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7

Cao, Xiwang, and Peipei Wang. "Primitive elements with prescribed trace." Applicable Algebra in Engineering, Communication and Computing 25, no. 5 (2014): 339–45. http://dx.doi.org/10.1007/s00200-014-0228-1.

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8

Chou, Wun-Seng, and Stephen D. Cohen. "Primitive Elements with Zero Traces." Finite Fields and Their Applications 7, no. 1 (2001): 125–41. http://dx.doi.org/10.1006/ffta.2000.0284.

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9

Brunner, A. M., R. G. Burns, and Sheila Oates-Williams. "On Almost Primitive Elements of Free Groups With an Application to Fuchsian Groups." Canadian Journal of Mathematics 45, no. 2 (1993): 225–54. http://dx.doi.org/10.4153/cjm-1993-011-9.

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AbstractAn element of a free group F is called almost primitive in F, if it is primitive in every proper subgroup containing it, though not in F itself. Several examples of almost primitive elements (APEs) are exhibited. The main results concern the behaviour of proper powers wℓ of certain APEs w in a free group F (and, more generally, in free products of cycles) with respect to any subgroup H containing such a power “minimally“: these assert, in essence, that either such powers of w behave in H as do powers of primitives of F, or, if not, then they “almost” do so and furthermore H must then h

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10

Onoda, Nobuharu, Takasi Sugatani, and Ken-ichi Yoshida. "Accurate Elements and Super-Primitive Elements over Rings." Journal of Algebra 245, no. 1 (2001): 370–94. http://dx.doi.org/10.1006/jabr.2001.8930.

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11

Xiang, Zhong, Yujia Shen, Zhitao Cheng, Miao Ma, and Feng Lin. "Periodic Pattern Detection of Printed Fabric Based on Deep Learning Algorithm." Journal of Physics: Conference Series 2148, no. 1 (2022): 012013. http://dx.doi.org/10.1088/1742-6596/2148/1/012013.

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Abstract Printed fabric patterns contain multiple repeat pattern primitives, which have a significant impact on fabric pattern design in the textile industry. The pattern primitive is often composed of multiple elements, such as color, form, and texture structure. Therefore, the more pattern elements it contains, the more complex the primitive is. In order to segment fabric primitives, this paper proposes a novel convolutional neural network (CNN) method with spatial pyramid pooling module as a feature extractor, which enables to learn the pattern feature information and determine whether the

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12

Anju and R. K. Sharma. "On primitive normal elements over finite fields." Asian-European Journal of Mathematics 11, no. 02 (2018): 1850031. http://dx.doi.org/10.1142/s1793557118500316.

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Let [Formula: see text] be an extension of the field [Formula: see text] of degree [Formula: see text] where [Formula: see text] for some positive integer [Formula: see text] and prime [Formula: see text] In this paper, we establish a sufficient condition for the existence of a primitive element [Formula: see text] such that [Formula: see text] is also primitive as well as a primitive normal element [Formula: see text] of [Formula: see text] over [Formula: see text] such that [Formula: see text] is primitive.

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13

Schutte, H. J. "Primitiewe elemente vir kommutatiewe ringuitbreidings." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 10, no. 2 (1991): 67–71. http://dx.doi.org/10.4102/satnt.v10i2.489.

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The existence of primitive elements for integral domain extensions is considered with reference to the well known theorem about primitive elements for field extensions. Primitive elements for extensions of a commutative ring R with identity are considered, where R has only a finite number of minimal prime ideals with zero intersection. This case is reduced to the case for ring extensions of integral domains.

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14

Yokoyama, Kazuhiro, Masayuki Noro, and Taku Takeshima. "Computing primitive elements of extension fields." Journal of Symbolic Computation 8, no. 6 (1989): 553–80. http://dx.doi.org/10.1016/s0747-7171(89)80061-6.

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15

GREITHER, CORNELIUS, and TOUFIK ZAÏMI. "CM FIELDS WITHOUT UNIT-PRIMITIVE ELEMENTS." Bulletin of the Australian Mathematical Society 96, no. 3 (2017): 398–99. http://dx.doi.org/10.1017/s0004972717000661.

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This is an addendum to a recent paper by Zaïmi, Bertin and Aljouiee [‘On number fields without a unit primitive element’, Bull. Aust. Math. Soc.93 (2016), 420–432], giving the answer to a question asked in that paper, together with some historical connections.

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16

Burillo, J., and E. Ventura. "COUNTING PRIMITIVE ELEMENTS IN FREE GROUPS." Electronic Notes in Discrete Mathematics 10 (November 2001): 50–53. http://dx.doi.org/10.1016/s1571-0653(04)00357-9.

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17

Gow, Rod, and John Sheekey. "On primitive elements in finite semifields." Finite Fields and Their Applications 17, no. 2 (2011): 194–204. http://dx.doi.org/10.1016/j.ffa.2010.11.003.

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18

Mikhalev, A. A., A. V. Mikhalev, A. A. Chepovskiy, and K. Champagnier. "Primitive elements of free nonassociative algebras." Journal of Mathematical Sciences 156, no. 2 (2009): 320–35. http://dx.doi.org/10.1007/s10958-008-9269-y.

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19

Kharchenko, V. K. "An algebra of skew primitive elements." Algebra and Logic 37, no. 2 (1998): 101–26. http://dx.doi.org/10.1007/bf02671596.

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20

KANEMITSU, MITSUO, JUNRO SATO, and KEN-ICHI YOSHIDA. "Some theorems concerning anti-integral, super-primitive and ultra-primitive elements." Mathematical journal of Ibaraki University 31 (1999): 33–36. http://dx.doi.org/10.5036/mjiu.31.33.

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21

Mikhalev, Alexander A., та Jie-Tai Yu. "Primitive, Almost Primitive, Test, and Δ-Primitive Elements of Free Algebras with the Nielsen–Schreier Property". Journal of Algebra 228, № 2 (2000): 603–23. http://dx.doi.org/10.1006/jabr.2000.8288.

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22

Hazarika, Himangshu, and Dhiren Kumar Basnet. "On Existence of Primitive Normal Elements of Cubic Form over Finite Fields." Algebra Colloquium 29, no. 01 (2022): 151–66. http://dx.doi.org/10.1142/s1005386722000128.

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For a prime [Formula: see text]and a positive integer[Formula: see text], let [Formula: see text] and [Formula: see text] be the extension field of [Formula: see text]. We derive a sufficient condition for the existence of a primitive element [Formula: see text] in[Formula: see text] such that [Formula: see text] is also a primitive element of [Formula: see text], a sufficient condition for the existence of a primitive normal element [Formula: see text] in [Formula: see text] over [Formula: see text] such that [Formula: see text] is a primitive element of [Formula: see text], and a sufficient

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23

Cohen, Stephen D., Hariom Sharma, and Rajendra Sharma. "Primitive values of rational functions at primitive elements of a finite field." Journal of Number Theory 219 (February 2021): 237–46. http://dx.doi.org/10.1016/j.jnt.2020.09.017.

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24

Khorin, Pavel A., Alexey P. Porfirev, and Svetlana N. Khonina. "Composite Diffraction-Free Beam Formation Based on Iteratively Calculated Primitives." Micromachines 14, no. 5 (2023): 989. http://dx.doi.org/10.3390/mi14050989.

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To form a diffraction-free beam with a complex structure, we propose to use a set of primitives calculated iteratively for the ring spatial spectrum. We also optimized the complex transmission function of the diffractive optical elements (DOEs), which form some primitive diffraction-free distributions (for example, a square or/and a triangle). The superposition of such DOEs supplemented with deflecting phases (a multi-order optical element) provides to generate a diffraction-free beam with a more complex transverse intensity distribution corresponding to the composition of these primitives. Th

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25

Drensky, Vesselin. "Additive primitive length in relatively free algebras." International Journal of Algebra and Computation 29, no. 05 (2019): 849–59. http://dx.doi.org/10.1142/s0218196719500310.

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The additive primitive length of an element [Formula: see text] of a relatively free algebra [Formula: see text] in a variety of algebras [Formula: see text] is equal to the minimal number [Formula: see text] such that [Formula: see text] can be presented as a sum of [Formula: see text] primitive elements. We give an upper bound for the additive primitive length of the elements in the [Formula: see text]-generated polynomial algebra over a field of characteristic 0, [Formula: see text]. The bound depends on [Formula: see text] and on the degree of the element. We show that if the field has mor

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26

Kong, Yingying, and Lining Jiang. "B-Fredholm elements in primitive C*-algebras." Open Mathematics 20, no. 1 (2022): 1394–406. http://dx.doi.org/10.1515/math-2022-0511.

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Abstract Let A {\mathcal{A}} be a unital primitive C ∗ \ast -algebra. This article studies the properties of the B-Fredholm elements, the B-Weyl elements and the B-Browder elements in A {\mathcal{A}} . Particularly, this article describes the B-Fredholm element as the sum of a Fredholm element and a nilpotent element. In addition, the socle of A {\mathcal{A}} is characterized by the B-Fredholm elements.

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27

Rakviashvili, G. "Primitive elements of free Lie $p$-algebras." Tbilisi Mathematical Journal 8, no. 2 (2015): 35–40. http://dx.doi.org/10.1515/tmj-2015-0008.

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28

Puder, D., and C. Wu. "Growth of primitive elements in free groups." Journal of the London Mathematical Society 90, no. 1 (2014): 89–104. http://dx.doi.org/10.1112/jlms/jdu009.

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29

Öğüşlü, Nazar Şahin, and Naime Ekici. "k-Primitivity and images of primitive elements." Journal of Algebra and Its Applications 15, no. 07 (2016): 1650126. http://dx.doi.org/10.1142/s0219498816501267.

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Let [Formula: see text] be a free Lie algebra of finite rank [Formula: see text] [Formula: see text]. We give another proof of the following criterion which is proven by Mikhalev and Zolotykh, using the idea of [Formula: see text]-primitivity: An endomorphism of [Formula: see text] preserving primitivity of elements is an automorphism.

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30

Dobbs, David E., and Evan Houston. "On sums and products of primitive elements." Communications in Algebra 45, no. 1 (2016): 357–70. http://dx.doi.org/10.1080/00927872.2016.1175459.

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31

Domínguez, J. M., and M. A. Mulero. "Primitive elements in rings of continuous functions." Topology and its Applications 157, no. 3 (2010): 522–29. http://dx.doi.org/10.1016/j.topol.2009.10.009.

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32

Bremser, Priscilla S., and Javier Gomez-Calderon. "Polynomials and primitive elements in Galois rings." Journal of Number Theory 41, no. 2 (1992): 172–77. http://dx.doi.org/10.1016/0022-314x(92)90118-9.

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33

Cohen, Stephen D. "Primitive elements and polynomials with arbitrary trace." Discrete Mathematics 83, no. 1 (1990): 1–7. http://dx.doi.org/10.1016/0012-365x(90)90215-4.

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34

Shpilrain, Vladimir. "Generalized primitive elements of a free group." Archiv der Mathematik 71, no. 4 (1998): 270–78. http://dx.doi.org/10.1007/s000130050264.

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35

Shestakov, Ivan P., and Ualbai U. Umirbaev. "Free Akivis Algebras, Primitive Elements, and Hyperalgebras." Journal of Algebra 250, no. 2 (2002): 533–48. http://dx.doi.org/10.1006/jabr.2001.9123.

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36

Maisuradze, M. V., and А. А. Mikhalev. "Primitive elements of free non-associative algebras over finite fields." Программирование, no. 2 (April 15, 2024): 84–92. http://dx.doi.org/10.31857/s0132347424020115.

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The representation of elements of free non-associative algebras as a set of multidimensional tables of coefficients is defined. An operation for finding partial derivatives for elements of free non-associative algebras in the same form is considered. Using this representation, a criterion of primitivity for elements of lengths 2 and 3 in terms of matrix ranks, as well as a primitivity test for elements of arbitrary length, is derived. This test makes it possible to estimate the number of primitive elements in free non-associative algebras with two generators over a finite field. The proposed r

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37

Klimakov, Andrey. "Primitivity rank of elements of free algebras of Schreier varieties." Journal of Algebra and Its Applications 15, no. 02 (2015): 1650036. http://dx.doi.org/10.1142/s0219498816500365.

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D. Puder defined the primitivity rank of elements of free groups [Primitive words, free factors and measure preservation, Israel J. Math.201(1) (2014) 25–73], we give a similar definition for free algebras of Schreier varieties and prove properties of a primitivity rank using the properties of the almost primitive elements.

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38

Szaniawski, Hubert, and Stefan Bengtson. "Origin of euconodont elements." Journal of Paleontology 67, no. 4 (1993): 640–54. http://dx.doi.org/10.1017/s0022336000024963.

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Primitive euconodont elements from the Upper Cambrian of Sweden are investigated histologically and compared with co-occurring elements of paraconodonts. The proposed close relationship between the two groups is confirmed. Typical euconodont and paraconodont elements are bridged by intermediate forms. The ontogenetic development of the early euconodont elements shows striking similarities to the evolutionary development from paraconodonts to euconodonts, suggesting that evolution generally followed a peramorphic pattern (“recapitulation”). The conodont crown originated through extension of the

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39

DRENSKY, VESSELIN, and JIE-TAI YU. "PRIMITIVE ELEMENTS OF FREE METABELIAN ALGEBRAS OF RANK TWO." International Journal of Algebra and Computation 13, no. 01 (2003): 17–33. http://dx.doi.org/10.1142/s021819670300133x.

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Let F(x,y) be a relatively free algebra of rank 2 in some variety of algebras over a field K of characteristic 0. In this paper we consider the problem whether p(x,y) ∈ F(x,y) is a primitive element (i.e. an automorphic image of x): (i) If F(x,y)/(p(x,y)) ≅ F(z), the relatively free algebra of rank 1 (ii) If p(f,g) is primitive for some injective endomorphism (f,g) of F(x,y) (iii) If p(x,y) is primitive in a relatively free algebra of larger rank. These problems have positive solutions for polynomial algebras in two variables. We give the complete answer for the free metabelian associative and

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40

Gupta, C. K., N. D. Gupta, and V. A. Roman'kov. "Primitivity in Free Groups and Free Metabelian Groups." Canadian Journal of Mathematics 44, no. 3 (1992): 516–23. http://dx.doi.org/10.4153/cjm-1992-033-0.

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AbstractLet Mn, c denote the free n-generator metabelian nilpotent group of class c. For m ≤ n – 2, every primitive system of m elements of Mn, c can be lifted to a primitive system of m elements of the absolutely free group Fn of rank n. The restriction on m cannot be improved.

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41

Bhandari, N. "Primitive Matter in Meteorites." Symposium - International Astronomical Union 120 (1987): 485–91. http://dx.doi.org/10.1017/s0074180900154506.

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A large number of elements in certain meteorites have isotopic composition different from that existing in rocks of the earth or the moon. Excess amounts of some isotopes, which are radiogenic daughters, are attributed to the in situ decay of their parent nuclide. Material containing radioactive parents is believed to have been injected into the condensing solar nebula, from astrophysical sites of their production shortly before formation of these grains. Other isotopic anomalies do not show mass dependent pattern which is characteristic of chemical fractionation. They must be primary isotopic

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42

Cohen, Stephen. "Kloosterman sums and primitive elements in Galois fields." Acta Arithmetica 94, no. 2 (2000): 173–201. http://dx.doi.org/10.4064/aa-94-2-173-201.

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43

Malvenuto, C., and C. Reutenauer. "Primitive elements of the Hopf algebras of tableaux." European Journal of Combinatorics 98 (December 2021): 103381. http://dx.doi.org/10.1016/j.ejc.2021.103381.

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44

Remondino, F., D. Lo Buglio, N. Nony, and L. De Luca. "DETAILED PRIMITIVE-BASED 3D MODELING OF ARCHITECTURAL ELEMENTS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XXXIX-B5 (July 28, 2012): 285–90. http://dx.doi.org/10.5194/isprsarchives-xxxix-b5-285-2012.

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45

Khadir, Omar. "Insecure primitive elements in an ElGamal signature protocol." Journal of Discrete Mathematical Sciences and Cryptography 18, no. 3 (2015): 237–45. http://dx.doi.org/10.1080/09720529.2014.927648.

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46

Cohen, Stephen D., Tomás Oliveira e Silva, and Tim Trudgian. "On consecutive primitive elements in a finite field." Bulletin of the London Mathematical Society 47, no. 3 (2015): 418–26. http://dx.doi.org/10.1112/blms/bdv018.

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47

Kikumasa, Isao, and Takasi Nagahara. "Primitive elements of Galois extensions of finite fields." Proceedings of the American Mathematical Society 115, no. 3 (1992): 593. http://dx.doi.org/10.1090/s0002-9939-1992-1081697-8.

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48

Mikhalev, Alexander A., and Andrej A. Zolotykh. "Automorphisms and primitive elements of free lie superalgebras." Communications in Algebra 22, no. 14 (1994): 5889–901. http://dx.doi.org/10.1080/00927879408825168.

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49

Kapetanakis, Giorgos. "Normal bases and primitive elements over finite fields." Finite Fields and Their Applications 26 (March 2014): 123–43. http://dx.doi.org/10.1016/j.ffa.2013.12.002.

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50

Cohen, Stephen D., and Gary L. Mullen. "Primitive elements in finite fields and costas arrays." Applicable Algebra in Engineering, Communication and Computing 2, no. 4 (1992): 297–99. http://dx.doi.org/10.1007/bf01614150.

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