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Perfect rectangular bands of inverse monoids

Authors
Journal
Journal of Pure and Applied Algebra
0022-4049
Publisher
Elsevier
Publication Date
Volume
40
Identifiers
DOI: 10.1016/0022-4049(86)90037-x

Abstract

Abstract Representations for the free rectangular band of inverse semigroups on a set and the free perfect rectangular band of inverse monoids on a set as quotients of suitable free unary semigroups are provided. It is shown that every rectangular band of inverse semigroups may be embedded in a perfect rectangular band of inverse monoids and that the free rectangular band of inverse semigroups on a set X may be embedded in a natural way in the free perfect rectangular band of inverse monoids on X. A modified version of Rasin's representation of the free completely simple semigroup on a set is discussed.

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