On the Brandt λ⁰-extensions of monoids with zero

الأصل · EN

We study algebraic properties of the Brandt λ⁰-extensions of monoids with zero and non-trivial homomorphisms between the Brandt λ⁰-extensions of monoids with zero. We introduce finite, compact topological Brandt λ⁰-extensions of topological semigroups and countably compact topological Brandt λ⁰-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 λ⁰-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 λ⁰-extensions of topological monoids with zeros.