Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T01:48:29.963Z Has data issue: false hasContentIssue false
  • English
  • Français

Algebras with a Diagonable Subspace whose Centralizer Satisfies a Polynomial Identity

Published online by Cambridge University Press:  20 November 2018

E. G. Goodaire
E. G. Goodaire*
Affiliation:
Memorial University of Newfoundland, St. John's, Newfoundland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The literature concerning rings with polynomial identity contains several theorems in which the existence of a polynomial identity on a subring implies the existence of such an identity on the ring itself. Belluce and Jain showed in 1968 that a prime ring will satisfy a polynomial identity provided it contains a right ideal with zero left annihilator which satisfies a polynomial identity [2].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 277 - 283
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Amitsur, S. A., Rings with involution, Israel J. Math. 6 (1968), 99–106.Google Scholar
2. Belluce, L. P. and Jain, S. K., Prime rings with a one-sided ideal satisfying a polynomial identity, Pac. J. Math. 24 (1968), 421–424.Google Scholar
3. Goodaire, E. G., Irreducible representations of algebras, Can. J. Math. 26 (1974), 1118–1129.Google Scholar
4. Herstein, I. N., Noncommutative rings, Carus Mathematical Monographs, Math. Assoc, of Amer. (Wiley, New York, 1968).Google Scholar
5. Jacobson, N., Structure of rings, Coll. Pub. 37, Amer. Math. Soc. (1964).Google Scholar
6. Martindale, W. S., III, Prime rings satisfying a generalized polynomial identity, J. of Alg. 12 (1969), 576–584.Google Scholar
7. Montgomery, S., Centralizers satisfying polynomial identities, Israel J. Math. 18 (1974), 207–219.Google Scholar
8. Montgomery, Susan and Smith, Martha K., Algebras with a separable subalgebra whose centralizer satisfies a polynomial identity, Comm. in Alg. 3 (2) (1975), 151–168.Google Scholar
9. Rowen, L., Some results on the center of a ring with polynomial identity, Bull. Amer. Math. Soc. 79 (1973), 219–223.Google Scholar
10. Smith, Martha K., Rings with an integral element whose centralizer satisfies a polynomial identity, Duke Math. J. 8 (1975), 137–149.Google Scholar