When is the Jacobson radical of a semigroup ring of a commutative semigroup homogeneous?
نویسندگان
چکیده
منابع مشابه
THE LEFT REGULAR REPRESENTATION OF A COMMUTATIVE SEPARATIVE SEMIGROUP
In this paper, a commutative semigroup will be written as a disjoint union of its cancellative subsemigroups. Based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. Finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.
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Munn [11] proved that the Jacobson radical of a commutative semigroup ring is nil provided that the radical of the coefficient ring is nil. This was generalized, for semigroup algebras satisfying polynomial identities, by Okniński [14] (cf. [15, Chapter 21]), and for semigroup rings of commutative semigroups with Noetherian rings of coefficients, by Jespers [4]. It would be interesting to obtai...
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Given a semigroup S, we prove that if the upper nilradical Nil∗(R) is homogeneous whenever R is an S-graded ring, then the semigroup S must be cancelative and torsion-free. In case S is commutative the converse is true. Analogs of these results are established for other radicals and ideals. We also describe a large class of semigroups S with the property that whenever R is a Jacobson radical ri...
متن کاملOn the Multiplicative Semigroup of a Commutative Ring
There seems to be no approach in the literature to a general theory of the structural restrictions which a semigroup must satisfy to be the multiplicative part of a ring. Johnson has treated the case that, as in Boolean rings, the addition is uniquely determined by the multiplication [l]. I do not know whether the present theorem extends to the noncommutative case. I am indebted to John Rainwat...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1987
ISSN: 0021-8693
DOI: 10.1016/0021-8693(87)90155-4