On the Brandt $λ^0$-extensions of monoids with zero

Details On the Brandt $λ^0$-extensions of monoids with zero On the Brandt $λ^0$-extensions of monoids with zero

2009-10-03

arxiv.org/abs/0910.0535v1

Semigroup Forum 80:1 (2010), 8-32.

Mathematics

Group Theory

Scientific paper

10.1007/s00233-009-9191-8

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.

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