Clifford semigroups as functors and their cohomology |
| |
Authors: | Elton Pasku |
| |
Affiliation: | 1.Departamenti i Matematik?s, Fakulteti i Shkencave t? Natyr?s,Universiteti i Tiran?s,Tiran?,Albania |
| |
Abstract: | We prove that the category of Clifford semigroups and prehomomorphisms CSP\mathcal{CSP} is isomorphic to a certain subcategory of the category of diagrams over groups. Under this isomorphism, Clifford semigroups
are identified with certain functors. As an application of the isomorphism theorem, we show that the category with objects
commutative inverse semigroups having the same semilattice of idempotents and with morphisms, the inverse semigroup homomorphisms
that fix the semilattice, imbeds into a category of right modules over a certain ring. Also we find a very close relationship
between the cohomology groups of a commutative inverse monoid and the cohomology groups of the colimit group of the functor
giving the monoid. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|