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On the Jacobson radical of semigroup rings of commutative semigroups

Published online by Cambridge University Press:  24 October 2008

A. V. Kelarev
A. V. Kelarev
Affiliation:
Department of Mathematics and Mechanics, Ural State University, Lenina 51, Sverdlovsk, 620083, U.S.S.R.
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Extract

Many authors have considered the radicals of semigroup rings of commutative semigroups. A list of the papers pertaining to this field is contained in [4]. In [1] Amitsur proved that, for any associative ring R and for every free commutative semigroup S, the equalities B(RS) = B(R)S and L(RS) = L(R)S hold, where B is the Baer radical and L is the Levitsky radical. A natural problem which arises is to describe semigroup rings RS such that π(RS) = π(R)S, where π is one of the most important radicals. For the Baer and Levitsky radicals and commutative semigroups a complete solution of the above problem follows from theorems 2·8 and 3·1 of [15].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 3 , November 1990 , pp. 429 - 433
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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