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1999•International Journal of Algebra and ComputationRequires access

PROPER WEAKLY LEFT AMPLE SEMIGROUPS

Gracinda M. S. Gomes, Victoria Gould

Open publisher page 41 citations

Abstract

Much of the structure theory of inverse semigroups is based on constructing arbitrary inverse semigroups from groups and semilattices. It is known that E-unitary (or proper) inverse semigroups may be described as P-semigroups (McAlister), or inverse subsemigroups of semidirect products of a semilattice by a group (O'Carroll) or C u -semigroups built over an inverse category acted upon by a group (Margolis and Pin). On the other hand, every inverse semigroup is known to have an E-unitary inverse cover (McAlister). The aim of this paper is to develop a similar theory for proper weakly left ample semigroups, a class with properties echoing those of inverse semigroups. We show how the structure of semigroups in this class is based on constructing semigroups from unipotent monoids and semilattices. The results corresponding to those of McAlister, O'Carroll and Margolis and Pin are obtained.

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What this paper is about

Much of the structure theory of inverse semigroups is based on constructing arbitrary inverse semigroups from groups and semilattices. It is known that E-unitary (or proper) inverse semigroups may be described as P-semigroups (McAlister), or inverse subsemigroups of semidirect products of a semilattice by a group (O'Carroll) or C u -semigroups built over an inverse category acted upon by a group (Margolis and Pin). On the other hand, every inverse semigroup is known to have an E-unitary inverse cover (McAlister). The aim of this paper is to develop a similar theory for proper weakly left ample semigroups, a class with properties echoing those of inverse semigroups. We show how the structure of semigroups in this class is based on constructing semigroups from unipotent monoids and semilattices. The results corresponding to those of McAlister, O'Carroll and Margolis and Pin are obtained.

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Available abstract

Much of the structure theory of inverse semigroups is based on constructing arbitrary inverse semigroups from groups and semilattices. It is known that E-unitary (or proper) inverse semigroups may be described as P-semigroups (McAlister), or inverse subsemigroups of semidirect products of a semilattice by a group (O'Carroll) or C u -semigroups built over an inverse category acted upon by a group (Margolis and Pin). On the other hand, every inverse semigroup is known to have an E-unitary inverse cover (McAlister). The aim of this paper is to develop a similar theory for proper weakly left ample semigroups, a class with properties echoing those of inverse semigroups. We show how the structure of semigroups in this class is based on constructing semigroups from unipotent monoids and semilattices. The results corresponding to those of McAlister, O'Carroll and Margolis and Pin are obtained.

Key concepts: Mathematics, Inverse semigroup, Semilattice, Special classes of semigroups, Inverse element, Krohn–Rhodes theory, Inverse, Pure mathematics

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