Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
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01 Jan 2011
TL;DR: The class (resp., t-class) semigroup is the semigroup of the isomorphy classes of the nonzero fractional ideals with the operation induced by ideal (t-) multiplication.
Abstract: The class (resp., t-class) semigroup of an integral domain is the semigroup of the isomorphy classes of the nonzero fractional ideals (resp., t-ideals) with the operation induced by ideal (t-) multiplication. This paper surveys recent literature which studies ring-theoretic conditions that reflect reciprocally in the Clifford property of the class (resp., t-class) semigroup. Precisely, it examines integral domains with Clifford class (resp., t-class) semigroup and describes their idempotent elements and the structure of their associated constituent groups.
4 citations
TL;DR: In this paper, the inverse monoid of local automorphisms of a semigroup S is defined as an isomorphism between two subsemigroups of this semigroup.
Abstract: A semigroup S is called permutable if $$ \rho $$
◦ σ = σ ◦ $$ \rho $$
for any pair of congruences $$ \rho $$
, σ on S. A local automorphism of the semigroup S is defined as an isomorphism between two subsemigroups of this semigroup. The set of all local automorphisms of a semigroup S with respect to an ordinary operation of composition of binary relations forms an inverse monoid of local automorphisms. We present a classification of all finite nilsemigroups for which the inverse monoid of local automorphisms is permutable.
4 citations
TL;DR: In this paper, it was shown that every non-degenerate irreducible homomorphism from the multiplicative semigroup of all n-by-n matrices over an algebraically closed field of characteristic zero to the semigroup m-bym matrices is reducible.
4 citations
TL;DR: In this article, the authors define the Andre]Quillen cohomology T s T A, A; k n G 0, A. The first three modules are important for the deformation theory of A or its geometric equivalent Spec A: T 1 equals the set of infinitesimal deformaA tions, T 0 describes their automorphisms, and T 2 contains the obstructions A A for lifting infiniteimal deformations to larger base spaces.
4 citations
4 citations