Relevant bibliographies by topics / Multiplicative inverse element

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  1. Journal articles
  2. Dissertations / Theses
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  4. Conference papers

Academic literature on the topic 'Multiplicative inverse element'

Author: Grafiati
Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "Multiplicative inverse element"

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Blyth, T. S., and M. H. Almeida Santos. "On weakly multiplicative inverse transversals." Proceedings of the Edinburgh Mathematical Society 37, no. 1 (February 1994): 91–99. http://dx.doi.org/10.1017/s001309150001871x.

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We show that an inverse transversal of a regular semigroup is multiplicative if and only if it is both weakly multiplicative and a quasi-ideal. Examples of quasi-ideal inverse transversals that are not multiplicative are known. Here we give an example of a weakly multiplicative inverse transversal that is not multiplicative. An interesting feature of this example is that it also serves to show that, in an ordered regular semigroup in which every element x has a biggest inverse x0, the mapping x↦x00 is not in general a closure; nor is x↦x** in a principally ordered regular semigroup.
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Cherubini, A., and A. Varisco. "Rings satisfying certain conditions either on subsemigroups or on endomorphisms." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 2 (April 1986): 194–202. http://dx.doi.org/10.1017/s1446788700027178.

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AbstractWe characterize rings whose multiplicative subsemigroups containing 0 and the additive inverse of each element are subrings. In addition we consider commutative rings for which every non-constant multiplicative endormorphism that preserves additive inverses is a ring endomorphism, and we show that they belong to one of three easily-described classes of rings.
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Saito, Tatsuhiko. "Naturally ordered regular semigroups with maximum inverses." Proceedings of the Edinburgh Mathematical Society 32, no. 1 (February 1989): 33–39. http://dx.doi.org/10.1017/s001309150000688x.

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Let S be a regular semigroup. An inverse subsemigroup S° of S is called an inverse transversal if S° contains a unique inverse of each element of S. An inverse transversal S° of S is called multiplicative if x°xyy° is an idempotent of S° for every x, y∈S, where x° denotes the unique inverse of x∈S in S°. In Section 1, we obtain a necessary and sufficient condition in order for inverse transversals to be multiplicative.
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Blyth, T. S., and M. H. Almeida Santos. "A simplistic approach to inverse transversals." Proceedings of the Edinburgh Mathematical Society 39, no. 1 (February 1996): 57–69. http://dx.doi.org/10.1017/s0013091500022781.

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An inverse transversal of a regular semigroup S is an inverse subsemigroup that contains precisely one inverse of each element of S. In the literature there are three known types of inverse transversal, namely those that are multiplicative, those that are weakly multiplicative, and those that form quasi-ideals. Here, by considering natural ways in which certain words can be simplified, we reveal four new types of inverse transversal. All of these can be illustrated nicely in examples that are based on 2 × 2 matrices.
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Sheibani, Abdolyousefi. "P-Hirano inverses in rings." Filomat 34, no. 13 (2020): 4473–82. http://dx.doi.org/10.2298/fil2013473s.

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We introduce and study a new class of generalized inverses in rings. An element a in a ring R has p-Hirano inverse if there exists b ? R such that bab = b,b ? comm2(a),(a2-ab)k ? J(R) for some k ? N. We prove that a ? R has p-Hirano inverse if and only if there exists p = p2 ? comm2(a) such that (a2-p)k ? J(R) for some k ? N. Multiplicative and additive properties for such generalized inverses are thereby obtained. We then completely determine when a 2 x 2 matrix over local rings has p-Hirano inverse.
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Saito, Tatsuhiko. "Construction of regular semigroups with inverse transversals." Proceedings of the Edinburgh Mathematical Society 32, no. 1 (February 1989): 41–51. http://dx.doi.org/10.1017/s0013091500006891.

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Let S be a regular semigroup. An inverse subsemigroup S° of S is an inverse transversal if |V(x)∩S°| = 1 for each x∈S, where V(x) denotes the set of inverses of x. In this case, the unique element of V(x)∩S° is denoted by x°, and x°° denotes (x°)–1. Throughout this paper S denotes a regular semigroup with an inverse transversal S°, and E(S°) = E° denotes the semilattice of idempotents of S°. The sets {e∈S:ee° = e} and {f∈S:f°f=f} are denoted by Is and Λs, respectively, or simply I and Λ. Though each element of these sets is idempotent, they are not necessarily sub-bands of S. When both I and Λ are sub-bands of S, S° is called an S-inverse transversal. An inverse transversal S° is multiplicative if x°xyy°∈E°, and S° is weakly multiplicative if (x°xyy°)°∈E° for every x, y∈S. A band B is left [resp. right] regular if e f e = e f [resp. e f e = f e], and B is left [resp. right] normal if e f g = e g f [resp. e f g = f e g] for every e, f, g∈B. A subset Q of S is a quasi-ideal of S if QSQ ⊆ S.
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Grošek, Otokar, and Tomáš Fabšič. "Computing multiplicative inverses in finite fields by long division." Journal of Electrical Engineering 69, no. 5 (September 1, 2018): 400–402. http://dx.doi.org/10.2478/jee-2018-0059.

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Abstract We study a method of computing multiplicative inverses in finite fields using long division. In the case of fields of a prime order p, we construct one fixed integer d(p) with the property that for any nonzero field element a, we can compute its inverse by dividing d(p) by a and by reducing the result modulo p. We show how to construct the smallest d(p) with this property. We demonstrate that a similar approach works in finite fields of a non-prime order, as well. However, we demonstrate that the studied method (in both cases) has worse asymptotic complexity than the extended Euclidean algorithm.
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8

Gould, Victoria. "Semigroups of left quotients—the uniqueness problem." Proceedings of the Edinburgh Mathematical Society 35, no. 2 (June 1992): 213–26. http://dx.doi.org/10.1017/s0013091500005496.

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Let S be a subsemigroup of a semigroup Q. Then Q is a semigroup of left quotients of S if every element of Q can be written as a*b, where a lies in a group -class of Q and a* is the inverse of a in this group; in addition, we insist that every element of S satisfying a weak cancellation condition named square-cancellable lie in a subgroup of Q.J. B. Fountain and M. Petrich gave an example of a semigroup having two non-isomorphic semigroups of left quotients. More positive results are available if we restrict the classes of semigroups from which the semigroups of left quotients may come. For example, a semigroup has at most one bisimple inverse ω-semigroup of left quotients. The crux of the matter is the restrictions to a semigroup S of Green's relations ℛ and ℒ in a semigroup of quotients of S. With this in mind we give necessary and sufficient conditions for two semigroups of left quotients of S to be isomorphic under an isomorphism fixing S pointwise.The above result is then used to show that if R is a subring of rings Q1 and Q2 and the multiplicative subsemigroups of Q1 and Q2 are semigroups of left quotients of the multiplicative semigroup of R, then Ql and Q2 are isomorphic rings.
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Dey, Sankhanil, and Ranjan Ghosh. "Mathematical Method to Search for Monic Irreducible Polynomials with Decimal Equivalents of Polynomials over Galois Field GF(pq)." Circulation in Computer Science 2, no. 11 (December 20, 2017): 17–22. http://dx.doi.org/10.22632/ccs-2017-252-68.

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Substitution boxes or S-boxes play a significant role in encryption and decryption of bit level plaintext and cipher-text respectively. Irreducible Polynomials (IPs) have been used to construct 4-bit or 8-bit substitution boxes in many cryptographic block ciphers. In Advance Encryption Standard the 8-bit the elements S-box have been obtained from the Multiplicative Inverse (MI) of elemental polynomials (EPs) of the 1st IP over Galois field GF(28) by adding an additive element. In this paper a mathematical method and the algorithm of the said method with the discussion of the execution time of the algorithm, to obtain monic IPs over Galois field GF(pq) have been illustrated with example. The method is very similar to polynomial multiplication of two polynomials over Galois field GF(pq) but has a difference in execution. The decimal equivalents of polynomials have been used to identify Basic Polynomials (BPs), EPs, IPs and Reducible polynomials (RPs). The monic RPs have been determined by this method and have been cancelled out to produce monic IPs. The non-monic IPs have been obtained with multiplication of α where α GF(pq) and assume values from 2 to (p-1) to monic IPs.
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Zheleznyak, Аlexander V. "Multiplicative property of series used in the Nevanlinna-Pick problem." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 9, no. 1 (2022): 37–45. http://dx.doi.org/10.21638/spbu01.2022.104.

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In the paper we obtained substantially new sufficient condition for negativity of coefficients of power series inverse to series with positive ones. It has been proved that element-wise product of power series retains this property. In particular, it gives rise to generalization of the classical Hardy theorem about power series. These results are generalized for cases of series with multiple variables. Such results are useful in Nevanlinna – Pick theory. For example, if function k(x, y) can be represented as power series Pn≥0 an(x¯y)n, an > 0, and reciprocal function 1/k(x, y) can be represented as power series Pn≥0 bn(x¯y)n such that bn < 0, n > 0, then k(x, y) is a reproducing kernel function for some Hilbert space of analytic functions in the unit disc D with Nevanlinna – Pick property. The reproducing kernel 1/(1 − x¯y) of the classical Hardy space H2(D) is a prime example for our theorems.
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Dissertations / Theses on the topic "Multiplicative inverse element"

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Онай, Микола Володимирович. "Методи та засоби підвищення ефективності реалізації обчислювальних операцій у скінченних полях." Doctoral thesis, Київ, 2017. https://ela.kpi.ua/handle/123456789/20968.

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У дисертаційній роботі вирішено актуальну науково-прикладну задачу – підвищення продуктивності систем цифрової обробки даних та криптографічних перетворень, забезпечення завадостійкості зберігання і передачі даних за рахунок створення ефективних технічних засобів для виконання обчислень у скінченних полях шляхом структурно-логічної оптимізації архітектур апаратних засобів, що реалізують процеси виконання операцій у полях Галуа. Запропоновано метод виконання операцій над елементами поля GF(2m). Особливістю даного методу, на відміну від існуючих, є застосування табличного зберігання елементів поля у многочленному та степеневому їх поданні з можливістю розрідженого формування таблиці елементів поля, що зменшує витрати пам’яті для її зберігання. Розроблений метод забезпечує зростання швидкодії на 15% порівняно з існуючим методом. Запропоновано модифікацію методу піднесення до степеня елементів поля GF(p) з ковзним вікном, яка забезпечує приріст швидкодії на 7-9 %. Спроектовано на ПЛІС фірми Xilinx процесор Галуа, що орієнтований на виконання операцій у скінченних полях виду GF(p) та GF(2m). Запропоновано програмістську модель процесора Галуа, яка дозволяє розробляти програмне забезпечення довільної складності мовою Асемблера проце-сора Галуа.
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Book chapters on the topic "Multiplicative inverse element"

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Rodriguez Lucatero, Carlos. "Application of Discrete Mathematics for Programming Discrete Mathematics Calculations." In New Trends in Combinatorics - Theory, Algorithms, Applications [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.102990.

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In the discrete mathematics courses, topics, such as the calculation of the element in any position of a sequence of numbers generated by some recurrence relation, calculation of multiplicative inverses in algebraic ring structures modulo a number n, obtaining the complete list of combinations without repetition, for which you can take advantage of the computing power of computers and perform such calculations using computer programs in some programming language. The implementations of these calculations can be carried out in many ways and therefore their algorithmic performance can be very varied. In this chapter, I propose to illustrate by means of some Matlab programs, how the use of results of the same discrete mathematics allows to improve the algorithmic performance of said computer programs. Another topic addressed in regular discrete mathematics courses where calculations arise that could become very expensive both in time and in occupied space, if the calculations are implemented directly from the definitions is modular arithmetic. Such calculations can be carried out much more efficiently by making use of results from discrete mathematics and number theory. The application of these ideas will be developed in the following sections of this chapter.
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Conference papers on the topic "Multiplicative inverse element"

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de Araujo Ramos Neto, Otacilio, Antonio Carlos Cavalcanti, and Ruy Alberto Pisani Altafim. "Comparison between three RTL implementations of the multiplicative inverse calculation of galois field elements based on a standard cells library." In 2013 IEEE Computer Society Annual Symposium on VLSI (ISVLSI). IEEE, 2013. http://dx.doi.org/10.1109/isvlsi.2013.6654660.

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Wen, Zhao, He Chaohui, Chen Wei, Guo Xiaoqiang, Cong Peitian, Zhang Fengqi, and Chen Rongmei. "Single Event Effect Characteristics Analysis of Typical Circuit Elements in Spacecraft Power Systems." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-67728.

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Single event effect occurs when a single energetic particle penetrates sensitive nodes and deposits enough charge by ionization in semiconductor devices. It has become a major reliability concern for spaceflight. Single event effect characteristics analysis methods based on simulation are presented for typical circuit elements in spacecraft power systems. The failure mechanism and impact factors of single event burnout in trench power MOSFETs are investigated through numerical simulation. The broadening, quenching and capture of single event transients in combinational logics are analyzed by circuit simulation based on a coupled single event transient injection method. A behavioral modeling is introduced to predict single event effect sensitivity of the parallel to serial conversion circuit. The results show that ion-induced holes can spread efficiently to turn on the parasitic bipolar junction transistor and result in stronger carrier multiplication when the ion strikes at the center of the gate region in trench power MOSFETs. Increasing the depth of P+ plugs, decreasing the doping concentration of source regions and using lower drain bias voltages can mitigate single event burnout susceptibility. Using the same load capacitance for each stage inverter and selecting a suitable gate-width ratio are recommended to prevent single event transient broadening in inverter chains. Moreover, the reset pin of D flip-flops in the parallel to serial conversion circuit should be hardened by design according to the behavioral modeling results.
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