On the Brandt ${\lambda }^0$-extensions of monoids with zero

Abstract

We study algebraic properties of the Brandt ${\lambda }^0$-extensions of monoids with zero and non-trivial homomorphisms between the Brandt ${\lambda }^0$-extensions of monoids with zero. We introduce finite, compact topological Brandt ${\lambda }^0$-extensions of topological semigroups and countably compact topological Brandt ${\lambda }^0$-extensions of topological inverse semigroups in the class of topological inverse semigroups and establish the structure of such extensions and non-trivial continuous homomorphisms between such topological Brandt ${\lambda }^0$-extensions of topological monoids with zero. We also describe a category whose objects are ingredients in the constructions of finite (compact, countably compact) topological Brandt ${\lambda }^0$-extensions of topological monoids with zeros.

References in corpus (1)

• On countably compact 0-simple topological inverse semigroups