Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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TL;DR: In this paper, it was shown that if the semigroup ring is integrally closed, then it is a PMD if and only if is a commutative cancellative semigroup.
Abstract: Let be an integral domain, and let be a group of units of . Let = - {0} and = / be the commutative cancellative semigroup under = . We prove that = and that is a PMD (resp., GCD-domain, Mori domain, Krull domain, factorial domain) if and only if is a PMS(resp., GCD-semigroup, Mori semigroup, Krull semigroup, factorial semigroup). Let = be the group of units of . We also show that if is integrally closed, then D[], the semigroup ring of over , is an integrally closed domain with = ; hence is a PMD (resp., GCD-domain, Krull domain, factorial domain) if and only if is.
1 citations
Journal Article•
TL;DR: In this article, it was shown that a strongly qrpp semigroup is a right C-qrpp semiigroup if and only if it is a semilattice of direct products of a left R-cancellation semigroup and a right zero band.
Abstract: In this paper,we investigate the dual of left C-wrpp semigroups,namely,right C-qrpp semigroups.We establish some characterizations of right C-grpp semigroups.In particular,it is proved that a strongly qrpp semigroup is a right C-qrpp semigroup if and only if it is a semilattice of direct products of a left R-cancellation semigroup and a right zero band.
1 citations
TL;DR: In this article, the semigroup of primitive generalized circulant Boolean matrices is studied, and some algebraic properties of this semigroup are obtained, and an asymptotic formula for the cardinality of the semi-group is given.
Abstract: In this paper, the semigroup of primitive generalized circulant Boolean matrices is studied, and some algebraic properties of this semigroup are obtained. Also, an asymptotic formula for the cardinality of the semigroup is given.
1 citations
TL;DR: In this article, the authors give an example of a tight inverse semigroup which is not bisimple and not congruence-free, but is congruent with a tight semigroup.
Abstract: We give an example of a tight inverse semigroup which is not bisimple and not congruence-free.
1 citations
TL;DR: In this article, the authors give a description of regular elements of the semigroup B X (D) which are defined by semilattices of the class Σ2 (X, 8), for which intersection the minimal elements is not empty.
Abstract: The paper gives description of regular elements of the semigroup B X (D) which are defined by semilattices of the class Σ2 (X, 8), for which intersection the minimal elements is not empty. When X is a finite set, the formulas are derived, by means of which the number of regular elements of the semigroup is calculated. In this case the set of all regular elements is a subsemigroup of the semigroup B X (D) which is defined by semilattices of the class Σ2 (X, 8).
1 citations