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Journal articles on the topic '010101 Algebra and Number Theory'

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Published: 10 December 2022

Last updated: 19 July 2025

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1

W., H. C., and Michael Pohst. "Algorithmic Methods in Algebra and Number Theory." Mathematics of Computation 55, no. 192 (1990): 876. http://dx.doi.org/10.2307/2008461.

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2

Passow, Eli, and Theodore J. Rivlin. "Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory." Mathematics of Computation 58, no. 198 (1992): 859. http://dx.doi.org/10.2307/2153227.

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3

Askey, Richard. "CHEBYSHEV POLYNOMIALS From Approximation Theory to Algebra and Number Theory." Bulletin of the London Mathematical Society 23, no. 3 (1991): 311–12. http://dx.doi.org/10.1112/blms/23.3.311.

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4

Borwein, Peter B. "Chebyshev polynomials: From approximation theory to algebra and number theory." Journal of Approximation Theory 66, no. 3 (1991): 353. http://dx.doi.org/10.1016/0021-9045(91)90038-c.

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5

Charafi, A. "Chebyshev polynomials—From approximation theory to algebra and number theory." Engineering Analysis with Boundary Elements 9, no. 2 (1992): 190. http://dx.doi.org/10.1016/0955-7997(92)90065-f.

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6

DOMOKOS, MÁTYÁS, and VESSELIN DRENSKY. "CONSTRUCTIVE NONCOMMMUTATIVE INVARIANT THEORY." Transformation Groups 26, no. 1 (2021): 215–28. http://dx.doi.org/10.1007/s00031-021-09643-2.

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AbstractThe problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite-dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same group acting on the symmetric tensor algebra of the Lie algebra. This process is applied to prove a constructive Hilbert–Nagata Theorem (including degree bounds) for the algebra of invariants in a Lie nilpotent relatively free associative algebra endowed with an action induced by a representation of a reductive group.

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7

Bezushchak, O. O., and B. V. Oliynyk. "Algebraic theory of measure algebras." Reports of the National Academy of Sciences of Ukraine, no. 2 (May 3, 2023): 3–9. http://dx.doi.org/10.15407/dopovidi2023.02.003.

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A. Horn and A. Tarski initiated the abstract theory of measure algebras. Independently V. Sushchansky, B. Oliynyk and P. Cameron studied the direct limits of Hamming spaces. In the current paper, we introduce new examples of locally standard measure algebras and complete the classification of countable locally standard measure algebras. Countable unital locally standard measure algebras are in one-to-one correspondence with Steinitz numbers. Given a Steinitz number s such measure algebra is isomorphic to the Boolean algebra of s-periodic sequences of 0 and 1. Nonunital locally standard measure algebras are parametrized by pairs (s, r), where s is a Steinitz number and r is a real number greater or equal to 1. We also show that an arbitrary (not necessarily locally standard) measure algebra is embeddable in a metric ultraproduct of standard Hamming spaces. In other words, an arbitrary measure algebra is sofic.

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8

Charnow, A., and E. Charnow. "69.40 An Application of Algebra to Number Theory." Mathematical Gazette 69, no. 450 (1985): 292. http://dx.doi.org/10.2307/3617580.

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9

Бедратюк, Леонід Петрович, and Ганна Іванівна Бедратюк. "Computer algebra systems in the elementary number theory." Eastern-European Journal of Enterprise Technologies 6, no. 4(66) (2013): 10–13. http://dx.doi.org/10.15587/1729-4061.2013.18892.

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10

Cheung, Y. L. "Learning number theory with a computer algebra system." International Journal of Mathematical Education in Science and Technology 27, no. 3 (1996): 379–85. http://dx.doi.org/10.1080/0020739960270308.

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11

Yackel, C. A., and J. K. Denny. "Partial Fractions in Calculus, Number Theory, and Algebra." College Mathematics Journal 38, no. 5 (2007): 362–74. http://dx.doi.org/10.1080/07468342.2007.11922261.

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12

Gaj, Kris, and Rainer Steinwandt. "Hardware architectures for algebra, cryptology, and number theory." Integration 44, no. 4 (2011): 257–58. http://dx.doi.org/10.1016/j.vlsi.2011.04.002.

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13

Schultz, Kyle T. "Soft Drinks, Mind Reading, and Number Theory." Mathematics Teacher 103, no. 4 (2009): 278–83. http://dx.doi.org/10.5951/mt.103.4.0278.

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14

Schultz, Kyle T. "Soft Drinks, Mind Reading, and Number Theory." Mathematics Teacher 103, no. 4 (2009): 278–83. http://dx.doi.org/10.5951/mt.103.4.0278.

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15

Hartwig, Brian, and Paul Terwilliger. "The Tetrahedron algebra, the Onsager algebra, and the sl2 loop algebra." Journal of Algebra 308, no. 2 (2007): 840–63. http://dx.doi.org/10.1016/j.jalgebra.2006.09.011.

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16

Adachi, Takahide, Osamu Iyama, and Idun Reiten. "-tilting theory." Compositio Mathematica 150, no. 3 (2013): 415–52. http://dx.doi.org/10.1112/s0010437x13007422.

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AbstractThe aim of this paper is to introduce $\tau $-tilting theory, which ‘completes’ (classical) tilting theory from the viewpoint of mutation. It is well known in tilting theory that an almost complete tilting module for any finite-dimensional algebra over a field $k$ is a direct summand of exactly one or two tilting modules. An important property in cluster-tilting theory is that an almost complete cluster-tilting object in a 2-CY triangulated category is a direct summand of exactly two cluster-tilting objects. Reformulated for path algebras $kQ$, this says that an almost complete support tilting module has exactly two complements. We generalize (support) tilting modules to what we call (support) $\tau $-tilting modules, and show that an almost complete support $\tau $-tilting module has exactly two complements for any finite-dimensional algebra. For a finite-dimensional $k$-algebra $\Lambda $, we establish bijections between functorially finite torsion classes in $ \mathsf{mod} \hspace{0.167em} \Lambda $, support $\tau $-tilting modules and two-term silting complexes in ${ \mathsf{K} }^{\mathrm{b} } ( \mathsf{proj} \hspace{0.167em} \Lambda )$. Moreover, these objects correspond bijectively to cluster-tilting objects in $ \mathcal{C} $ if $\Lambda $ is a 2-CY tilted algebra associated with a 2-CY triangulated category $ \mathcal{C} $. As an application, we show that the property of having two complements holds also for two-term silting complexes in ${ \mathsf{K} }^{\mathrm{b} } ( \mathsf{proj} \hspace{0.167em} \Lambda )$.

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17

Hadas, Ofer, Anne Henke та Amitai Regev. "ℤ2-Graded Number Theory". Communications in Algebra 34, № 8 (2006): 3077–95. http://dx.doi.org/10.1080/00927870600640086.

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18

Gatermann, Karin, and Serkan Hosten. "Computational algebra for bifurcation theory." Journal of Symbolic Computation 40, no. 4-5 (2005): 1180–207. http://dx.doi.org/10.1016/j.jsc.2004.04.007.

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19

Solberg, Øyvind. "Hopf algebra constructions and representation theory." Communications in Algebra 17, no. 7 (1989): 1775–86. http://dx.doi.org/10.1080/00927878908823819.

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20

Feldvoss, Jörg, and Daniel K. Nakano. "Representation Theory of the Witt Algebra." Journal of Algebra 203, no. 2 (1998): 447–69. http://dx.doi.org/10.1006/jabr.1997.7343.

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21

Tang, Xin. "(Hopf) Algebra Automorphisms of the Hopf Algebra." Communications in Algebra 41, no. 8 (2013): 2996–3012. http://dx.doi.org/10.1080/00927872.2012.668992.

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22

Gao, Jining. "L∞ algebra structures from Lie algebra deformations." Journal of Pure and Applied Algebra 208, no. 3 (2007): 779–84. http://dx.doi.org/10.1016/j.jpaa.2006.03.016.

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23

Adin, Ron M., Alexander Postnikov, and Yuval Roichman. "Hecke Algebra Actions on the Coinvariant Algebra." Journal of Algebra 233, no. 2 (2000): 594–613. http://dx.doi.org/10.1006/jabr.2000.8441.

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24

Adamović, Dražen, and Ante Čeperić. "On Zhu's algebra and C2–algebra for symplectic fermion vertex algebra SF(d)+." Journal of Algebra 563 (December 2020): 376–403. http://dx.doi.org/10.1016/j.jalgebra.2020.07.019.

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25

Kleiner, Israel. "The Roots of Commutative Algebra in Algebraic Number Theory." Mathematics Magazine 68, no. 1 (1995): 3. http://dx.doi.org/10.2307/2691370.

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26

Sobczyk, Garret. "The Missing Spectral Basis in Algebra and Number Theory." American Mathematical Monthly 108, no. 4 (2001): 336. http://dx.doi.org/10.2307/2695240.

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27

Kleiner, Israel. "The Roots of Commutative Algebra in Algebraic Number Theory." Mathematics Magazine 68, no. 1 (1995): 3–15. http://dx.doi.org/10.1080/0025570x.1995.11996267.

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28

Sobczyk, Garret. "The Missing Spectral Basis in Algebra and Number Theory." American Mathematical Monthly 108, no. 4 (2001): 336–46. http://dx.doi.org/10.1080/00029890.2001.11919757.

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29

Patil, D. P., C. R. Pranesachar, and Renuka Ravindran. "The work of lagrange in number theory and algebra." Resonance 11, no. 4 (2006): 10–25. http://dx.doi.org/10.1007/bf02835727.

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30

Varro, Richard. "Gonosomal algebra." Journal of Algebra 447 (February 2016): 1–30. http://dx.doi.org/10.1016/j.jalgebra.2015.09.023.

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31

Szántó, Csaba. "A GENERIC HALL ALGEBRA OF THE KRONECKER ALGEBRA." Communications in Algebra 33, no. 8 (2005): 2519–40. http://dx.doi.org/10.1081/agb-200065132.

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32

Nichols, Warren D., and M. Bettina Richmond. "The grothendieck algebra of a hopf algebra, i." Communications in Algebra 26, no. 4 (1998): 1081–95. http://dx.doi.org/10.1080/00927879808826185.

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33

Costa, R., L. S. Ikemoto, and A. Suazo. "On the multiplication algebra of a bernstein algebra*." Communications in Algebra 26, no. 11 (1998): 3727–36. http://dx.doi.org/10.1080/00927879808826369.

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34

Ziplies, Dieter. "Abelianizing the divided powers algebra of an algebra." Journal of Algebra 122, no. 2 (1989): 261–74. http://dx.doi.org/10.1016/0021-8693(89)90215-9.

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35

Parshall, Karen Hunger, A. N. Kolmogorov, and A. P. Yushkevich. "Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory Probability Theory." American Mathematical Monthly 101, no. 4 (1994): 369. http://dx.doi.org/10.2307/2975639.

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36

Karve, Aneesh, and Sebastian Pauli. "GiANT: Graphical Algebraic Number Theory." Journal de Théorie des Nombres de Bordeaux 18, no. 3 (2006): 721–27. http://dx.doi.org/10.5802/jtnb.569.

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37

Granville, Andrew. "Pretentiousness in analytic number theory." Journal de Théorie des Nombres de Bordeaux 21, no. 1 (2009): 159–73. http://dx.doi.org/10.5802/jtnb.664.

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38

Graham, Ronald L., Jeffrey C. Lagarias, Colin L. Mallows, Allan R. Wilks, and Catherine H. Yan. "Apollonian circle packings: number theory." Journal of Number Theory 100, no. 1 (2003): 1–45. http://dx.doi.org/10.1016/s0022-314x(03)00015-5.

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39

Zhang, Hai Yan, and Xin Song Yang. "On Normal Sequence in Abelian Group C_n⊕C_{_n}." Advanced Materials Research 981 (July 2014): 255–57. http://dx.doi.org/10.4028/www.scientific.net/amr.981.255.

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Electronic information technology is based on expression, storage, transmission, and process of information. Information expression is usually generalized as information coding technology, one of whose heart theories is combinatorial number theory in algebra. In the process of storing, transmitting, and processing of electronic information technology, problems about encryption and safety need to use algebra theories of group, ring, and domain. It is thus clear that algebra is very important in electronic information theory. This paper makes use of abelian group basic theory of algebra, together with combination number theory, discusses construction problem of normal sequence in of abelian group, and gives several sufficient conditions for a guess establishment of W.D.Gao.

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40

Kanuni̇, Müge, and Murad Özaydin. "Cohn–Leavitt path algebras and the invariant basis number property." Journal of Algebra and Its Applications 18, no. 05 (2019): 1950086. http://dx.doi.org/10.1142/s0219498819500865.

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We give the necessary and sufficient condition for a separated Cohn–Leavitt path algebra of a finite digraph to have Invariant Basis Number (IBN). As a consequence, separated Cohn path algebras have IBN. We determine the non-stable K-theory of a corner ring in terms of the non-stable K-theory of the ambient ring. We give a necessary condition for a corner algebra of a separated Cohn–Leavitt path algebra of a finite graph to have IBN. We provide Morita equivalent rings which are non-IBN, but are of different types.

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41

Murphy, Gerald J. "The C*-Algebra of a Function Algebra." Integral Equations and Operator Theory 47, no. 3 (2003): 361–74. http://dx.doi.org/10.1007/s00020-002-1167-y.

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42

Shomron, Noam, and Beresford N. Parlett. "Linear Algebra meets Lie Algebra: The Kostant–Wallach theory." Linear Algebra and its Applications 431, no. 10 (2009): 1745–67. http://dx.doi.org/10.1016/j.laa.2009.06.007.

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43

Beidar, K. I., and M. A. Chebotar. "When Is a Graded PI Algebra a PI Algebra?" Communications in Algebra 31, no. 6 (2003): 2951–64. http://dx.doi.org/10.1081/agb-120021901.

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44

Costa, R., and A. Suazo. "The multiplication algebra of a bernstein algebra: basic results." Communications in Algebra 24, no. 5 (1996): 1809–21. http://dx.doi.org/10.1080/00927879608825673.

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45

Zhang, Pu. "Indecomposables in the composition algebra of the kronecker algebra." Communications in Algebra 27, no. 10 (1999): 4633–39. http://dx.doi.org/10.1080/00927879908826720.

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46

Brown, Peter. "The Ext-Algebra of a Representation-Finite Biserial Algebra." Journal of Algebra 221, no. 2 (1999): 611–29. http://dx.doi.org/10.1006/jabr.1999.8001.

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47

Fialowski, Alice, and Friedrich Wagemann. "Associative algebra deformations of Connes–Moscovici's Hopf algebra H1." Journal of Algebra 323, no. 7 (2010): 2026–40. http://dx.doi.org/10.1016/j.jalgebra.2009.12.033.

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48

Angeltveit, Vigleik. "Uniqueness of MoravaK-theory." Compositio Mathematica 147, no. 2 (2010): 633–48. http://dx.doi.org/10.1112/s0010437x10005026.

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AbstractWe show that there is an essentially uniqueS-algebra structure on the MoravaK-theory spectrumK(n), whileK(n) has uncountably manyMUor$\widehat {E(n)}$-algebra structures. Here$\widehat {E(n)}$is theK(n)-localized Johnson–Wilson spectrum. To prove this we set up a spectral sequence computing the homotopy groups of the moduli space ofA∞structures on a spectrum, and use the theory ofS-algebrak-invariants for connectiveS-algebras found in the work of Dugger and Shipley [Postnikov extensions of ring spectra, Algebr. Geom. Topol.6(2006), 1785–1829 (electronic)] to show that all the uniqueness obstructions are hit by differentials.

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49

Carter, R. W. "Representation theory of the 0-Hecke algebra." Journal of Algebra 104, no. 1 (1986): 89–103. http://dx.doi.org/10.1016/0021-8693(86)90238-3.

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50

Zhu, Ping, and Yongzhi Cao. "Cyclotomic blob algebra and its representation theory." Journal of Pure and Applied Algebra 204, no. 3 (2006): 666–95. http://dx.doi.org/10.1016/j.jpaa.2005.06.011.

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