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2005 | 3 | 4 | 644-653
Tytuł artykułu

Centers in domains with quadratic growth

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let F be a field, and let R be a finitely-generated F-algebra, which is a domain with quadratic growth. It is shown that either the center of R is a finitely-generated F-algebra or R satisfies a polynomial identity (is PI) or else R is algebraic over F. Let r ∈ R be not algebraic over F and let C be the centralizer of r. It is shown that either the quotient ring of C is a finitely-generated division algebra of Gelfand-Kirillov dimension 1 or R is PI.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
4
Strony
644-653
Opis fizyczny
Daty
wydano
2005-12-01
online
2005-12-01
Twórcy
Bibliografia
  • [1] M. Artin, W. Schelter and J. Tate: “The centers of 3-dimensional Skylyanian algebras”, In: Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991), Perspect. Math., Vol. 15, Academic Press, San Diego, CA, 1994, pp. 1–10.
  • [2] M. Artin and J.T. Stafford: “Noncommutative graded domains with quadratic growth”, Invent. Math., Vol. 122(2), (1995), pp. 231–276. http://dx.doi.org/10.1007/BF01231444
  • [3] J.P. Bell: private communication.
  • [4] J.P. Bell and L.W. Small: “Centralizers in domains of Gelfand-Kirillov dimension 2”, Bull. London Math. Soc., Vol. 36(6), pp. 779–785.
  • [5] G.M. Bergman: A note of growth functions of algebras and semigroups, mimeographed notes, University of California, Berkeley, 1978.
  • [6] G. Krause and T. Lenagan: Growth of Algebras and Gelfand-Kirillov Dimension, Revised Edition, Graduate Studies in Mathematics, Vol. 22, American Society, Providence, 2000.
  • [7] M. Lothaire, Algebraic Combinatorics of Words, Cambridge University Press 2002.
  • [8] J.C. McConnel and J.C. Robson: Noncommutative Noetherian Rings, Wiley Interscience, Chichester, 1987.
  • [9] L.W. Small, J.T. Stafford and R.B. Warfield Jr: “Affine algebras of Gelfand-Kirillov dimension one are PI”, Math. Proc. Cambridge Phil. Soc., Vol. 97, (1984), pp. 407–414. http://dx.doi.org/10.1017/S0305004100062976
  • [10] L.W. Small and R.B. Warfield, Jr: “Prime affine algebras of Gelfand-Kirillov dimension one”, J. Algebra, Vol. 91, (1984) pp. 384–389. http://dx.doi.org/10.1016/0021-8693(84)90110-8
  • [11] S.P. Smith and J.J. Zhang: “A remark of Gelfand-Kirillov dimension”, Proc. Amer. Math. Soc., Vol. 126(2), (1998), pp. 349–352. http://dx.doi.org/10.1090/S0002-9939-98-04074-X
  • [12] A. Smoktunowicz: “On structure of domains with quadratic growth”, J. Algebra, Vol. 289(2), (2005), pp. 365–379. http://dx.doi.org/10.1016/j.jalgebra.2005.04.004
  • [13] J.T. Stafford and M. Van den Bergh: “Noncommutative curves and noncommutative surfaces”, Bull. Am. Math. Soc., Vol. 38(2), pp. 171–216.
  • [14] J.J. Zhang: “On lower transcendence degree”, Adv. Math., Vol. 139, (1998), pp. 157–193. http://dx.doi.org/10.1006/aima.1998.1749
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475624
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