Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-06-30T22:55:31.330Z Has data issue: false hasContentIssue false
  • English
  • Français

Commutativity theorems for rings with polynomial constraints on certain subsets

Published online by Cambridge University Press:  17 April 2009

Hiroaki Komatsu  and
Hisao Tominaga
Hiroaki Komatsu
Affiliation:
Department of Mathematics, Okayama University, Okayama, 700, Japan
Hisao Tominaga
Affiliation:
Department of Mathematics, Okayama University, Okayama, 700, Japan
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.

We prove several commutativity theorems for unital rings with polynomial constraints on certain subsets, which improve and generalise the recent results of Grosen, and Ashraf and Quadri.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 3 , June 1991 , pp. 451 - 462
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Abu-Khuzam, H., ‘Commutativity results for rings’, Bull. Austral. Math. Soc. 38 (1988), 191–195.CrossRefGoogle Scholar
[2]Ashraf, M. and Quadri, M.A., ‘On commutativity of rings with some polynomial constraints’, Bull. Austral. Math. Soc. 41 (1990), 201–206.CrossRefGoogle Scholar
[3]Belluse, L.P., Herstein, I.N. and Jam, S.K., ‘Generalized commutative rings’, Nagoya Math. J. 27 (1966), 1–5.CrossRefGoogle Scholar
[4]Grosen, J., Rings satisfying polynomial identities or constraints on certain subsets, Thesis (University of California, Santa Barbara, 1988).Google Scholar
[5]Herstein, I.N., ‘A commutativity theorem’, J. Algebra 38 (1976), 473–478.CrossRefGoogle Scholar
[6]Hirano, Y., Kobayashi, Y. and Tominaga, H., ‘Some polynomial identities and commutativity of s–unital rings’, Math. J. Okayama Univ. 24 (1982), 7–13.Google Scholar
[7]Hirano, Y., Tominaga, H. and Yaqub, A., ‘Some polynomial identities and commutativity of s–unital rings. II’, Math. J. Okayama Univ. 24 (1982), 111–115.Google Scholar
[8]Hongan, M., ‘A commutativity theorem for s–unital rings. II’, Math. J. Okayama Univ. 25 (1983), 19–22.Google Scholar
[9]Komatsu, H. and Tominaga, H., ‘Chacron's condition and commutativity theorems’, Math. J. Okayama Univ. 31 (1989), 101–120.Google Scholar
[10]Komatsu, H. and Tominaga, H., ‘Some commutativity theorems for left s–unital rings’, Resultate Math. 15 (1989), 335–342.CrossRefGoogle Scholar
[11]Streb, W., ‘Zur Struktur nichtkommutativer Ringe’, Math. J. Okayama Univ. 31 (1989), 135–140.Google Scholar