Noetherian properties of skew polynomial rings with binomial relations
Author:
Tatiana Gateva-Ivanova
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
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Abstract | References | Similar Articles | Additional Information
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.
- [Ap] J. Apel, Gröbnerbasen in nichtkommutativen Algebren und ihre anwendung, Dissertation A, Karl-Marx-Universität, Leipzig.
- [Art-S] Michael Artin and William F. Schelter, Graded algebras of global dimension 3, Adv. in Math. 66 (1987), no. 2, 171–216. MR 917738, https://doi.org/10.1016/0001-8708(87)90034-X
- [Berg] George M. Bergman, The diamond lemma for ring theory, Adv. in Math. 29 (1978), no. 2, 178–218. MR 506890, https://doi.org/10.1016/0001-8708(78)90010-5
- [Buch] 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)
- [G-I
] Tatiana Gateva-Ivanova, On the Noetherianity of some associative finitely presented algebras, J. Algebra 138 (1991), no. 1, 13–35. MR 1102566, https://doi.org/10.1016/0021-8693(91)90189-F
- [G-I
] 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
- [G-I
] -, Groebner bases in skew polynomial rings, preprint, Dept. of Math. Reports No. 8, University of Stockholm, 1992, pp. 1-33.
- [Go1] 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, https://doi.org/10.1007/BFb0082019
- [K-R-W] 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, https://doi.org/10.1016/S0747-7171(08)80003-X
- [Mor
] 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, https://doi.org/10.1007/3-540-51084-2_14
- [Mor
] T. Mora, Seven variations on standard bases, Univ. di Genova, Dipartimento di Matematica, N. 45 Preprint, 1988.
- [Sm-St] S. P. Smith and J. T. Stafford, Regularity of the four dimensional Sklyanin algebra, preprint, 1990.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1994-1173854-3
Article copyright:
© Copyright 1994
American Mathematical Society