Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-16T12:46:42.463Z Has data issue: false hasContentIssue false
  • English
  • Français

Hereditary radicals and bands of associative rings

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

A. V. Kelarev
A. V. Kelarev
Affiliation:
Department of Mathematics Ural State UniversityLenina 51 Sverdlovsk USSR 620083
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.

Bands of associative rings were introduced in 1973 by Weissglass. For the radicals playing most essential roles in the structure theory (in particular, for those of Jacobson, Baer, Levitsky, Koethe) it is shown how to find the radical of a band of rings. The technique of the general Kurosh-Amitsur radical theory is used to consider many radicals simultaneously.

MSC classification

Secondary: 20M25: Semigroup rings, multiplicative semigroups of rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 1 , August 1991 , pp. 62 - 72
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Andrunakievich, V. A. and Rjabuhin, Ju. M., Radicals of algebras and structure theory (Nauka, Moscow, 1979), in Russian.Google Scholar
[2]Chick, H. L. and Gardner, B. J., ‘The preservation of some ring properties by semilattice sums’, Comm. Algebra 15 (1987), 1667–1677.CrossRefGoogle Scholar
[3]Clifford, A. and Preston, G., The algebraic theory of semigroups, (Math. Surveys No. 7 Amer. Math. Soc., Providence, R.I., 1964).Google Scholar
[4]Gardner, B. J., ‘Radicals and supplementary semilattice sums of associative rings’, Pacific J. Math. 58 (1975), 387–392.CrossRefGoogle Scholar
[5]Kelarev, A. V., ‘Radicals and bands of associative algebras’, Algebra i logica (Novosibirsk) 28 (1989), 430–443.Google Scholar
[6]Kelarev, V. A., ‘Radicals of semigroup algebras of commutative semigroups’, Abstracts of XIX All-Union algebraic conference (Lvov, 1987), Vol. 2, 122, in Russian.Google Scholar
[7]Kelarev, A. V., ‘Radicals of semilattices of algebras and semigroup algebras’, Vestnik Moscov. Gos. Univ. No. 1 73 (1988), in Russian.Google Scholar
[8]Volkov, M. V. and Kelarev, A. V., ‘Varieties and bands of associative rings’, Izv. Vyssh. Učebn. Zaved. Mat. No. 9, (1986), 16–23, in Russian.Google Scholar
[9]Weissglass, J., ‘Semigroup rings and semilattice sums of rings’, Proc. Amer. Math. Soc. 39 (1973), 471–478.CrossRefGoogle Scholar