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

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Published: 10 December 2022

Last updated: 29 January 2023

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1

W., H. C., and Michael Pohst. "Algorithmic Methods in Algebra and Number Theory." Mathematics of Computation 55, no. 192 (October 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 (April 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 (May 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 (September 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 (January 1992): 190. http://dx.doi.org/10.1016/0955-7997(92)90065-f.

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6

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

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7

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) (December 16, 2013): 10–13. http://dx.doi.org/10.15587/1729-4061.2013.18892.

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8

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

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9

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

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10

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

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11

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

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12

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

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13

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

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14

Tang, Xin. "(Hopf) Algebra Automorphisms of the Hopf Algebra." Communications in Algebra 41, no. 8 (August 3, 2013): 2996–3012. http://dx.doi.org/10.1080/00927872.2012.668992.

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15

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

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16

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

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17

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

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18

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

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19

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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20

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

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21

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

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22

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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23

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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24

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 (May 2003): 1–45. http://dx.doi.org/10.1016/s0022-314x(03)00015-5.

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25

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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26

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

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27

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

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28

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

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29

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

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30

DOMOKOS, MÁTYÁS, and VESSELIN DRENSKY. "CONSTRUCTIVE NONCOMMMUTATIVE INVARIANT THEORY." Transformation Groups 26, no. 1 (February 24, 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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31

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

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32

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

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33

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

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34

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

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35

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

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36

Adachi, Takahide, Osamu Iyama, and Idun Reiten. "-tilting theory." Compositio Mathematica 150, no. 3 (December 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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37

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 (April 1994): 369. http://dx.doi.org/10.2307/2975639.

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38

Beidar, K. I., and M. A. Chebotar. "When Is a Graded PI Algebra a PI Algebra?" Communications in Algebra 31, no. 6 (January 7, 2003): 2951–64. http://dx.doi.org/10.1081/agb-120021901.

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39

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

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40

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

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41

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

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42

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

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43

Murphy, Gerald J. "The C*-Algebra of a Function Algebra." Integral Equations and Operator Theory 47, no. 3 (November 1, 2003): 361–74. http://dx.doi.org/10.1007/s00020-002-1167-y.

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44

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

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45

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

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46

López Franco, Ignacio L. "Formal Hopf algebra theory, II: Lax centres." Journal of Pure and Applied Algebra 213, no. 11 (November 2009): 2038–54. http://dx.doi.org/10.1016/j.jpaa.2009.03.011.

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47

Miyamoto, Masahiko. "Representation Theory of Code Vertex Operator Algebra." Journal of Algebra 201, no. 1 (March 1998): 115–50. http://dx.doi.org/10.1006/jabr.1997.7257.

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48

Niibori, Hidekazu, and Daisuke Sagaki. "Simplicity of a Vertex Operator Algebra Whose Griess Algebra is the Jordan Algebra of Symmetric Matrices." Communications in Algebra 38, no. 3 (March 16, 2010): 848–75. http://dx.doi.org/10.1080/00927870902828637.

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49

Choi, Seul Hee, Jongwoo Lee, and Ki-Bong Nam. "Algebra Versus Its Anti-symmetric Algebra." Algebra Colloquium 16, no. 04 (December 2009): 661–68. http://dx.doi.org/10.1142/s1005386709000625.

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For a given algebra A= 〈A,+,·〉, we can define its anti-symmetric algebra A-= 〈A-,+,[ , ]〉 using the commutator [ , ] of A, where the sets A and A- are the same. We show that there are isomorphic algebras A1 and A2 such that their anti-symmetric algebras are not isomorphic. We define a special type Lie algebra and show that it is simple.

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50

Belabas, Karim. "Topics in computational algebraic number theory." Journal de Théorie des Nombres de Bordeaux 16, no. 1 (2004): 19–63. http://dx.doi.org/10.5802/jtnb.433.

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