Results 121 to 130 of about 166 (160)

Arithmetical Semigroup Rings

Canadian Journal of Mathematics, 1980
Throughout this paper the ring R and the semigroup S are commutative with identity; moreover, it is assumed that S is cancellative, i.e., that S can be embedded in a group. The aim of this note is to determine necessary and sufficient conditions on R and S that the semigroup ring R[S] should be one of the following types of rings: principal ideal ring (
Hardy, Bonnie R., Shores, Thomas S.
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ON THE COEFFICIENT RING IN A SEMIGROUP RING

Mathematics of the USSR-Izvestiya, 1976
In this paper we study the concept of the invariance of a ring relative to a commutative semigroup. Invariance is proved for certain Prufer rings and affine algebras relative to semigroups of a special class.Bibliography: 11 titles.
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The semigroup ring of a restriction semigroup with an inverse skeleton

Semigroup Forum, 2014
The problem is to find conditions (necessary, sufficient) for a semigroup ring \(R(S)\) of a semigroup \(S\) to be semiprime, semiprimitive, prime, and primitive. The authors extend \textit{W. D. Munn}'s techniques [Proc. R. Soc. Edinb., Sect. A 107, 175-196 (1987; Zbl 0627.20041); and ibid. 115, No.
Gomes, Gracinda M. S., Santa-Clara, Catarina, Soares, Filipa   +2 more
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The regularity of munn rings and semigroup rings

Acta Mathematica Sinica, 1995
A ring means an associative ring, modules over rings are left ones. A ring \(R\) is said to have the strong IBN property iff every free \(R\)- module of any rank \(n\) cannot be generated by less than \(n\) elements. Let \(M_n (R)\) denote the full matrix ring of degree \(n\) over \(R\).
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Semigroup rings over semiprime ring semigroups

2019
We consider semigroup rings over a particular class of semigroups: those semigroups which arise as the multiplicative semigroup of a ring.
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Technique of semigroup ring theory: Regular semigroup rings

Journal of Mathematical Sciences, 1999
Let \(S\) be a semigroup and \(G\) a subgroup of \(S\). Let \(R\) be a ring (perhaps, without unity) and \(R'\) a subring of \(R\). The author gives connections between properties of the group ring \(RG\) and the semigroup ring \(RS\), and also the semigroup rings \(RS\) and \(R'S\).
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Radicals of semigroup rings of commutative semigroups

Mathematical Proceedings of the Cambridge Philosophical Society, 1986
In this paper we determine radicals of semigroup rings R[S] where R is an associative, not necessarily commutative, ring and S is a commutative semigroup. We will restrict ourselves to the prime radical P, the Levitzki radical L and the Jacobson radical J. At the end we will also give a few comments on the Brown-McCoy radical U.
Okniński, J., Wauters, P.
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Coinduction for semigroup-graded rings

Communications in Algebra, 1999
We describe the graded-simple modules over a semigroup-graded ring in terms of the simple modules over various component subrings. Our method utilizes the coinduction functors Coindx .
ABRAMS G., MENINI, Claudia
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Hausdorff series in a semigroup ring

International Journal of Algebra and Computation, 2020
Let [Formula: see text] and [Formula: see text] be the semigroup rings spanned on the right zero semigroup [Formula: see text], and on the left zero semigroup [Formula: see text], respectively, together with the identity element [Formula: see text].
Findik, Sehmus, Kelekci, Osman
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Semigroups and rings

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1978
In a previous publication [1] we considered the structure of a fragmented ring and of its multiplicative semigroup. In the present publication we consider, in a purely semigroup-theoretic context, some ideas related to those in [1]. As shown by an example, the semigroups we consider need not be the multiplicative semigroup of a ring.
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