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Artykuły w czasopismach na temat „Algebraic number theory”

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Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 2 marca 2023

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1

Blackmore, G. W., I. N. Stewart i D. O. Tall. "Algebraic Number Theory". Mathematical Gazette 73, nr 463 (marzec 1989): 65. http://dx.doi.org/10.2307/3618234.

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2

S., R., i Michael E. Pohst. "Computational Algebraic Number Theory." Mathematics of Computation 64, nr 212 (październik 1995): 1763. http://dx.doi.org/10.2307/2153389.

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3

Karve, Aneesh, i Sebastian Pauli. "GiANT: Graphical Algebraic Number Theory". Journal de Théorie des Nombres de Bordeaux 18, nr 3 (2006): 721–27. http://dx.doi.org/10.5802/jtnb.569.

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4

Lenstra Jr., H. W. "Algorithms in Algebraic Number Theory". Bulletin of the American Mathematical Society 26, nr 2 (1.10.1992): 211–45. http://dx.doi.org/10.1090/s0273-0979-1992-00284-7.

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5

Platonov, V. P., i A. S. Rapinchuk. "Algebraic groups and number theory". Russian Mathematical Surveys 47, nr 2 (30.04.1992): 133–61. http://dx.doi.org/10.1070/rm1992v047n02abeh000879.

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6

Appleby, Marcus, Steven Flammia, Gary McConnell i Jon Yard. "SICs and Algebraic Number Theory". Foundations of Physics 47, nr 8 (24.04.2017): 1042–59. http://dx.doi.org/10.1007/s10701-017-0090-7.

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7

Belabas, Karim. "Topics in computational algebraic number theory". Journal de Théorie des Nombres de Bordeaux 16, nr 1 (2004): 19–63. http://dx.doi.org/10.5802/jtnb.433.

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8

Schoof, Ren\'e. "Book Review: Algorithmic algebraic number theory". Bulletin of the American Mathematical Society 29, nr 1 (1.07.1993): 111–14. http://dx.doi.org/10.1090/s0273-0979-1993-00392-6.

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9

Krishna, Amalendu, i Jinhyun Park. "Algebraic cobordism theory attached to algebraic equivalence". Journal of K-Theory 11, nr 1 (luty 2013): 73–112. http://dx.doi.org/10.1017/is013001028jkt210.

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AbstractBased on the algebraic cobordism theory of Levine and Morel, we develop a theory of algebraic cobordism modulo algebraic equivalence.We prove that this theory can reproduce Chow groups modulo algebraic equivalence and the semi-topological K0-groups. We also show that with finite coefficients, this theory agrees with the algebraic cobordism theory.We compute our cobordism theory for some low dimensional varieties. The results on infinite generation of some Griffiths groups by Clemens and on smash-nilpotence by Voevodsky and Voisin are also lifted and reinterpreted in terms of this cobordism theory.

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10

Cremona, J. E., i Henri Cohen. "A Course in Computational Algebraic Number Theory". Mathematical Gazette 78, nr 482 (lipiec 1994): 221. http://dx.doi.org/10.2307/3618596.

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11

Wójcik, J. "On a problem in algebraic number theory". Mathematical Proceedings of the Cambridge Philosophical Society 119, nr 2 (luty 1996): 191–200. http://dx.doi.org/10.1017/s0305004100074090.

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Let K be an algebraic number field. If q is a prime ideal of the ring of integers of K and α is a number of K prime to q then Mq(α) denotes the multiplicative group generated by α modulo q. In the paper [5] there is the remark: ‘We do not know whether for all a, b, c ∈ ℚ with abc ≠ 0, |a| ≠ 1,|b| ≠ 1,|c| ≠ 1 there exist infinitely many primes q with Mq (a) = Mq (b) = Mq (c).’

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12

Lagarias, Jeffrey C., i Yang Wang. "Haar Bases forL2( ) and Algebraic Number Theory". Journal of Number Theory 76, nr 2 (czerwiec 1999): 330–36. http://dx.doi.org/10.1006/jnth.1998.2353.

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13

Aoki, Masao. "Deformation theory of algebraic stacks". Compositio Mathematica 141, nr 01 (1.12.2004): 19–34. http://dx.doi.org/10.1112/s0010437x04000806.

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14

Thompson, Robert C. "Editorial announcement: Algebraic graph theory". Linear and Multilinear Algebra 28, nr 1-2 (październik 1990): 1. http://dx.doi.org/10.1080/03081089008818025.

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15

Tamme, Georg. "Excision in algebraic -theory revisited". Compositio Mathematica 154, nr 9 (6.08.2018): 1801–14. http://dx.doi.org/10.1112/s0010437x18007236.

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By a theorem of Suslin, a Tor-unital (not necessarily unital) ring satisfies excision in algebraic$K$-theory. We give a new and direct proof of Suslin’s result based on an exact sequence of categories of perfect modules. In fact, we prove a more general descent result for a pullback square of ring spectra and any localizing invariant. Our descent theorem contains not only Suslin’s result, but also Nisnevich descent of algebraic$K$-theory for affine schemes as special cases. Moreover, the role of the Tor-unitality condition becomes very transparent.

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16

Mandal, Satya, i Yong Yang. "Intersection theory of algebraic obstructions". Journal of Pure and Applied Algebra 214, nr 12 (grudzień 2010): 2279–93. http://dx.doi.org/10.1016/j.jpaa.2010.02.027.

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17

Levine, Marc. "Intersection theory in algebraic cobordism". Journal of Pure and Applied Algebra 221, nr 7 (lipiec 2017): 1645–90. http://dx.doi.org/10.1016/j.jpaa.2016.12.022.

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18

Stengle, Gillbert. "Algebraic theory of differential inequalities". Communications in Algebra 19, nr 6 (styczeń 1991): 1743–63. http://dx.doi.org/10.1080/00927879108824227.

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19

Perucca, Antonella, i Pietro Sgobba. "Kummer theory for number fields and the reductions of algebraic numbers". International Journal of Number Theory 15, nr 08 (19.08.2019): 1617–33. http://dx.doi.org/10.1142/s179304211950091x.

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For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov–Ribet method) of the fact that if [Formula: see text] is a finitely generated and torsion-free multiplicative subgroup of a number field [Formula: see text] having rank [Formula: see text], then the ratio between [Formula: see text] and the Kummer degree [Formula: see text] is bounded independently of [Formula: see text]. We then apply this result to generalize to higher rank a theorem of Ziegler from 2006 about the multiplicative order of the reductions of algebraic integers (the multiplicative order must be in a given arithmetic progression, and an additional Frobenius condition may be considered).

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20

Dai, Shouxin, i Marc Levine. "Connective Algebraic K-theory". Journal of K-Theory 13, nr 1 (2.01.2014): 9–56. http://dx.doi.org/10.1017/is013012007jkt249.

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AbstractWe examine the theory of connective algebraic K-theory, , defined by taking the −1 connective cover of algebraic K-theory with respect to Voevodsky's slice tower in the motivic stable homotopy category. We extend to a bi-graded oriented duality theory when the base scheme is the spectrum of a field k of characteristic zero. The homology theory may be viewed as connective algebraic G-theory. We identify for X a finite type k-scheme with the image of in , where is the abelian category of coherent sheaves on X with support in dimension at most n; this agrees with the (2n,n) part of the theory of connective algebraic K-theory defined by Cai. We also show that the classifying map from algebraic cobordism identifies with the universal oriented Borel-Moore homology theory having formal group law u + υ − βuυ with coefficient ring ℤ[β]. As an application, we show that every pure dimension d finite type k-scheme has a well-defined fundamental class [X]CK in ΩdCK(X), and this fundamental class is functorial with respect to pull-back for l.c.i. morphisms.

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21

Baumslag, Gilbert, Alexei Myasnikov i Vladimir Remeslennikov. "Algebraic Geometry over Groups I. Algebraic Sets and Ideal Theory". Journal of Algebra 219, nr 1 (wrzesień 1999): 16–79. http://dx.doi.org/10.1006/jabr.1999.7881.

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22

van Hoeij, Mark, i Vivek Pal. "Isomorphisms of algebraic number fields". Journal de Théorie des Nombres de Bordeaux 24, nr 2 (2012): 293–305. http://dx.doi.org/10.5802/jtnb.797.

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23

Aragona, J., A. R. G. Garcia i S. O. Juriaans. "Algebraic theory of Colombeauʼs generalized numbers". Journal of Algebra 384 (czerwiec 2013): 194–211. http://dx.doi.org/10.1016/j.jalgebra.2013.03.005.

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24

Yuan, Pingzhi. "On algebraic approximations of certain algebraic numbers". Journal of Number Theory 102, nr 1 (wrzesień 2003): 1–10. http://dx.doi.org/10.1016/s0022-314x(03)00068-4.

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25

Lagarias, Jeffrey C., i Yang Wang. "Haar Bases forL2(Rn) and Algebraic Number Theory". Journal of Number Theory 57, nr 1 (marzec 1996): 181–97. http://dx.doi.org/10.1006/jnth.1996.0042.

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26

Kelly, Shane, i Matthew Morrow. "K-theory of valuation rings". Compositio Mathematica 157, nr 6 (20.05.2021): 1121–42. http://dx.doi.org/10.1112/s0010437x21007119.

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We prove several results showing that the algebraic $K$-theory of valuation rings behaves as though such rings were regular Noetherian, in particular an analogue of the Geisser–Levine theorem. We also give some new proofs of known results concerning cdh descent of algebraic $K$-theory.

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27

Ozan, Yildiray. "On algebraic K-theory of real algebraic varieties with circle action". Journal of Pure and Applied Algebra 170, nr 2-3 (maj 2002): 287–93. http://dx.doi.org/10.1016/s0022-4049(01)00129-3.

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28

Tanimoto, Ryuji. "Algebraic torus actions on affine algebraic surfaces". Journal of Algebra 285, nr 1 (marzec 2005): 73–97. http://dx.doi.org/10.1016/j.jalgebra.2004.10.021.

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29

Pezlar, Zdeněk. "Solving Diophantine Equations by Factoring in Number Fields". Journal of the ASB Society 2, nr 1 (27.12.2021): 29–34. http://dx.doi.org/10.51337/jasb20211227004.

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In this text we provide an introduction to algebraic number theory and show its applications in solving certain difficult diophantine equations. We begin with a quick summary of the theory of quadratic residues, before diving into a select few areas of algebraic number theory. Our article is accompanied by a couple of worked problems and exercises for the reader to tackle on their own.

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30

Duflot, Jeanne, i C. Tyrel Marak. "A filtration in algebraic K-theory". Journal of Pure and Applied Algebra 151, nr 2 (lipiec 2000): 135–62. http://dx.doi.org/10.1016/s0022-4049(99)00050-x.

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31

Dickmann, M., i F. Miraglia. "Algebraic K-theory of special groups". Journal of Pure and Applied Algebra 204, nr 1 (styczeń 2006): 195–234. http://dx.doi.org/10.1016/j.jpaa.2005.04.002.

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32

Kida, Masanari. "Kummer theory for norm algebraic tori". Journal of Algebra 293, nr 2 (listopad 2005): 427–47. http://dx.doi.org/10.1016/j.jalgebra.2005.06.035.

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33

Grayson, Daniel R. "Universal exactness in algebraic K-theory". Journal of Pure and Applied Algebra 36 (1985): 139–41. http://dx.doi.org/10.1016/0022-4049(85)90066-0.

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34

Shimakawa, Kazuhisa. "Multiple categories and algebraic K-theory". Journal of Pure and Applied Algebra 41 (1986): 285–304. http://dx.doi.org/10.1016/0022-4049(86)90114-3.

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35

Perucca, Antonella, i Pietro Sgobba. "Kummer Theory for Number Fields and the Reductions of Algebraic Numbers II". Uniform distribution theory 15, nr 1 (1.06.2020): 75–92. http://dx.doi.org/10.2478/udt-2020-0004.

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AbstractLet K be a number field, and let G be a finitely generated and torsion-free subgroup of K×. For almost all primes p of K, we consider the order of the cyclic group (G mod 𝔭), and ask whether this number lies in a given arithmetic progression. We prove that the density of primes for which the condition holds is, under some general assumptions, a computable rational number which is strictly positive. We have also discovered the following equidistribution property: if ℓe is a prime power and a is a multiple of ℓ (and a is a multiple of 4 if ℓ =2), then the density of primes 𝔭 of K such that the order of (G mod 𝔭) is congruent to a modulo ℓe only depends on a through its ℓ-adic valuation.

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36

Khanduja, Sudesh K. "The discriminant of compositum of algebraic number fields". International Journal of Number Theory 15, nr 02 (marzec 2019): 353–60. http://dx.doi.org/10.1142/s1793042119500167.

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For an algebraic number field [Formula: see text], let [Formula: see text] denote the discriminant of an algebraic number field [Formula: see text]. It is well known that if [Formula: see text] are algebraic number fields with coprime discriminants, then [Formula: see text] are linearly disjoint over the field [Formula: see text] of rational numbers and [Formula: see text], [Formula: see text] being the degree of [Formula: see text] over [Formula: see text]. In this paper, we prove that the converse of this result holds in relative extensions of algebraic number fields. We also give some more necessary and sufficient conditions for the analogue of the above equality to hold for algebraic number fields [Formula: see text] linearly disjoint over [Formula: see text].

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37

Kramer, Linus, i Katrin Tent. "Algebraic Polygons". Journal of Algebra 182, nr 2 (czerwiec 1996): 435–47. http://dx.doi.org/10.1006/jabr.1996.0179.

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38

Ensor, A. "Algebraic coalitions". algebra universalis 38, nr 1 (grudzień 1997): 1–14. http://dx.doi.org/10.1007/s000120050035.

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39

Abouzahra, M., i L. Lewin. "The polylogarithm in algebraic number fields". Journal of Number Theory 21, nr 2 (październik 1985): 214–44. http://dx.doi.org/10.1016/0022-314x(85)90052-6.

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40

Rausch, U. "Character Sums in Algebraic Number Fields". Journal of Number Theory 46, nr 2 (luty 1994): 179–95. http://dx.doi.org/10.1006/jnth.1994.1011.

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41

Fischler, Stéphane. "Orbits under algebraic groups and logarithms of algebraic numbers". Acta Arithmetica 100, nr 2 (2001): 167–87. http://dx.doi.org/10.4064/aa100-2-4.

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42

Nishioka, Kumiko. "Algebraic independence of certain power series of algebraic numbers". Journal of Number Theory 23, nr 3 (lipiec 1986): 354–64. http://dx.doi.org/10.1016/0022-314x(86)90080-6.

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43

Nauryzbayev, N. Zh, G. E. Taugynbayev i M. Beisenbek. "Application aspects of algebraic number theory in financial mathematics". Bulletin of L.N. Gumilyov Eurasian National University. Mathematics. Computer Sciences. Mechanics series 130, nr 1 (2020): 93–102. http://dx.doi.org/10.32523/2616-7182/2020-130-1-93-102.

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44

Kleiner, Israel. "The Roots of Commutative Algebra in Algebraic Number Theory". Mathematics Magazine 68, nr 1 (1.02.1995): 3. http://dx.doi.org/10.2307/2691370.

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45

Trotter, Hale. "Book Review: A course in computational algebraic number theory". Bulletin of the American Mathematical Society 31, nr 2 (1.10.1994): 312–19. http://dx.doi.org/10.1090/s0273-0979-1994-00542-7.

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46

Kleiner, Israel. "The Roots of Commutative Algebra in Algebraic Number Theory". Mathematics Magazine 68, nr 1 (luty 1995): 3–15. http://dx.doi.org/10.1080/0025570x.1995.11996267.

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47

Guàrdia, Jordi, Jesús Montes i Enric Nart. "Newton polygons of higher order in algebraic number theory". Transactions of the American Mathematical Society 364, nr 1 (1.01.2012): 361–416. http://dx.doi.org/10.1090/s0002-9947-2011-05442-5.

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48

Hong, Haibo, Licheng Wang, Haseeb Ahmad, Jing Li, Yixian Yang i Changzhong Wu. "Construction of DNA codes by using algebraic number theory". Finite Fields and Their Applications 37 (styczeń 2016): 328–43. http://dx.doi.org/10.1016/j.ffa.2015.10.008.

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49

Gauthier, Yvon. "On Cantor's normal form theorem and algebraic number theory". International Journal of Algebra 12, nr 3 (2018): 133–40. http://dx.doi.org/10.12988/ija.2018.8413.

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50

Guo, Xiao Qiang, i Zheng Jun He. "The Applications of Group Theory". Advanced Materials Research 430-432 (styczeń 2012): 1265–68. http://dx.doi.org/10.4028/www.scientific.net/amr.430-432.1265.

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Since the classification of finite simple groups completed last century, the applications of group theory are more and more widely. We first introduce the connection of groups and symmetry. And then we respectively introduce the applications of group theory in polynomial equation, algebraic topology, algebraic geometry , cryptography, algebraic number theory, physics and chemistry.

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