Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Noetherian properties of skew polynomial rings with binomial relations
HTML articles powered by AMS MathViewer

by Tatiana Gateva-Ivanova PDF
Trans. Amer. Math. Soc. 343 (1994), 203-219 Request permission

Abstract:

In this work we study standard finitely presented associative algebras over a fixed field K. A restricted class of skew polynomial rings with quadratic relations considered in an earlier work of M. Artin and W. Schelter will be studied. We call them binomial skew polynomial algebras. We establish necessary and sufficient conditions for such an algebra to be a Noetherian domain.
References
    J. Apel, Gröbnerbasen in nichtkommutativen Algebren und ihre anwendung, Dissertation A, Karl-Marx-Universität, Leipzig.
  • Michael Artin and William F. Schelter, Graded algebras of global dimension $3$, Adv. in Math. 66 (1987), no. 2, 171–216. MR 917738, DOI 10.1016/0001-8708(87)90034-X
  • George M. Bergman, The diamond lemma for ring theory, Adv. in Math. 29 (1978), no. 2, 178–218. MR 506890, DOI 10.1016/0001-8708(78)90010-5
    • B. Buchberger, An algorithm for finding a basis for the residue class ring of a zero-dimensional polynomial ideal, Ph.D. thesis, Univ. Innsbruck (Austria), Math. Inst., 1965, Aequationes Math. 4 (1970), 374-383. (German)
  • Tatiana Gateva-Ivanova, On the Noetherianity of some associative finitely presented algebras, J. Algebra 138 (1991), no. 1, 13–35. MR 1102566, DOI 10.1016/0021-8693(91)90189-F
  • Tatiana Gateva-Ivanova, Noetherian properties and growth of some associative algebras, Effective methods in algebraic geometry (Castiglioncello, 1990) Progr. Math., vol. 94, Birkhäuser Boston, Boston, MA, 1991, pp. 143–158. MR 1106419
    • —, Groebner bases in skew polynomial rings, preprint, Dept. of Math. Reports No. 8, University of Stockholm, 1992, pp. 1-33.
  • E. S. Golod, Standard bases and homology, Algebra—some current trends (Varna, 1986) Lecture Notes in Math., vol. 1352, Springer, Berlin, 1988, pp. 88–95. MR 981820, DOI 10.1007/BFb0082019
  • A. Kandri-Rody and V. Weispfenning, Noncommutative Gröbner bases in algebras of solvable type, J. Symbolic Comput. 9 (1990), no. 1, 1–26. MR 1044911, DOI 10.1016/S0747-7171(08)80003-X
  • Teo Mora, Groebner bases in noncommutative algebras, Symbolic and algebraic computation (Rome, 1988) Lecture Notes in Comput. Sci., vol. 358, Springer, Berlin, 1989, pp. 150–161. MR 1034727, DOI 10.1007/3-540-51084-2_{1}4
    • T. Mora, Seven variations on standard bases, Univ. di Genova, Dipartimento di Matematica, N. 45 Preprint, 1988. S. P. Smith and J. T. Stafford, Regularity of the four dimensional Sklyanin algebra, preprint, 1990.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 16P40
  • Retrieve articles in all journals with MSC: 16P40
Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 343 (1994), 203-219
  • MSC: Primary 16P40
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1173854-3
  • MathSciNet review: 1173854