Results 1  10
of
2,636
Identities of Regular Semigroup Rings
, 1998
"... The author proves that, if S is an FICsemigroup or a completely regular semigroup, and if RS is a ring with identity, then R<E(S)> is a ring with identity. ..."
Abstract
 Add to MetaCart
The author proves that, if S is an FICsemigroup or a completely regular semigroup, and if RS is a ring with identity, then R<E(S)> is a ring with identity.
A REGULARITY CRITERION FOR SEMIGROUP RINGS
"... Abstract. An analogue of the Kunz–Frobenius criterion for the regularity of a local ring in a positive characteristic is established for general commutative semigroup rings. Let S be a commutative semigroup (we always assume that S contains a neutral element), and K a field. For every m ∈ Z+ the ass ..."
Abstract
 Add to MetaCart
Abstract. An analogue of the Kunz–Frobenius criterion for the regularity of a local ring in a positive characteristic is established for general commutative semigroup rings. Let S be a commutative semigroup (we always assume that S contains a neutral element), and K a field. For every m ∈ Z
Certain Rings and Semigroups Examining the Regularity Property
"... A number of main properties of the commuting regular rings and commuting regular semigroups have been studied in this paper. Some significant results of which will be used for the commutative rings and a necessary and sufficient condition is given for a semigroup to be commuting regular. 1. ..."
Abstract
 Add to MetaCart
A number of main properties of the commuting regular rings and commuting regular semigroups have been studied in this paper. Some significant results of which will be used for the commutative rings and a necessary and sufficient condition is given for a semigroup to be commuting regular. 1.
The regular Property of Duo Semigroups and Duo Rings
"... Abstract: In mathematics, a semigroup is an algebraic structure that consists of a set together with an associative binary operation. A semigroup generalizes a monoid. As such, there might not exist an identity element. It also generalizes a group (a monoid with all inverses) to a type where every e ..."
Abstract
 Add to MetaCart
element need not have an inverse, which ascribes the name semigroup. The concept of a semigroup is very simple, but plays a predominant role in the development of Mathematics. This paper discusses in detail the regular property of duo semigroups and duo rings. 1.
Semigroups, Rings, and Markov Chains
, 2000
"... We analyze random walks on a class of semigroups called "leftregular bands." These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable and we calculate the eigenvalues and multi ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
We analyze random walks on a class of semigroups called "leftregular bands." These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable and we calculate the eigenvalues
IDEMPOTENTS OF COMMUTATIVE SEMIGROUP RINGS
"... Assume that R is a commutative ring (not necessarily with identity) and S is an additive abelian semigroup. Following the notation of Northcott in [16, page 128], we let R[X;S] denote the semigroup ring of S over R, and we write elements of R[X;S] in the form rl Xsl +..+ rn Xsn, where r i C R and s ..."
Abstract
 Add to MetaCart
Assume that R is a commutative ring (not necessarily with identity) and S is an additive abelian semigroup. Following the notation of Northcott in [16, page 128], we let R[X;S] denote the semigroup ring of S over R, and we write elements of R[X;S] in the form rl Xsl +..+ rn Xsn, where r i C R
ANNIHILATORSEMIGROUPS AND RINGS
"... Abstract. Let R be a commutative ring with 1. We define R to be an annihilatorsemigroup ring if R has an annihilatorsemigroup S, that is, (S, ·) is a multiplicative subsemigroup of (R, ·) with the property that for each r ∈ R there exists a unique s ∈ S with 0: r = 0: s. The quotient monoid R/ ≡ w ..."
Abstract
 Add to MetaCart
Abstract. Let R be a commutative ring with 1. We define R to be an annihilatorsemigroup ring if R has an annihilatorsemigroup S, that is, (S, ·) is a multiplicative subsemigroup of (R, ·) with the property that for each r ∈ R there exists a unique s ∈ S with 0: r = 0: s. The quotient monoid R
Commuting regular rings
"... Abstract. R is called commuting regular ring (resp. semigroup) if for each x; y 2 R there exists a 2 R such that xy = yxayx. In this paper, we introduce the concept of commuting regular rings (resp. semigroups) and study various properties of them. c ⃝ 2013 IAUCTB. All rights reserved. ..."
Abstract
 Add to MetaCart
Abstract. R is called commuting regular ring (resp. semigroup) if for each x; y 2 R there exists a 2 R such that xy = yxayx. In this paper, we introduce the concept of commuting regular rings (resp. semigroups) and study various properties of them. c ⃝ 2013 IAUCTB. All rights reserved.
NOTE ON INTEGRAL CLOSURES OF SEMIGROUP RINGS
, 1999
"... Abstract. Let S be a subsemigroup which contains 0 of a torsionfree abelian (additive) group. Then S is called a grading monoid (or a gmonoid). The group {s − s′s, s ′ ∈ S} is called the quotient group of S, and is denored by q(S). Let R be a commutative ring. The total quotient ring of R is den ..."
Abstract
 Add to MetaCart
is denoted by q(R). Throught the paper, we assume that a gmonoid properly contains {0}. A commutative ring is called a ring, and a nonzerodivisor of a ring is called a regular element of the ring. We consider integral elements over the semigroup ring R[X;S] of S over R. Let S be a gmonoid with quotient
Results 1  10
of
2,636