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2009•International Journal of Algebra and ComputationRequires access

A CHARACTERIZATION OF THE INVERSE MONOID OF BI-CONGRUENCES OF CERTAIN ALGEBRAS

Kalle Kaarli, L. Márki

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Abstract

This paper provides an abstract characterization of the inverse monoids that appear as monoids of bi-congruences of finite minimal algebras generating arithmetical varieties. As a tool, a matrix construction is introduced which might be of independent interest in inverse semigroup theory. Using this construction as well as Ramsey's theorem, we embed a certain kind of inverse monoid into a factorizable monoid of the same kind. As noticed by M. Lawson, this embedding entails that the embedded finite monoids have finite F-unitary cover.

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What this paper is about

This paper provides an abstract characterization of the inverse monoids that appear as monoids of bi-congruences of finite minimal algebras generating arithmetical varieties. As a tool, a matrix construction is introduced which might be of independent interest in inverse semigroup theory. Using this construction as well as Ramsey's theorem, we embed a certain kind of inverse monoid into a factorizable monoid of the same kind. As noticed by M. Lawson, this embedding entails that the embedded finite monoids have finite F-unitary cover.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper provides an abstract characterization of the inverse monoids that appear as monoids of bi-congruences of finite minimal algebras generating arithmetical varieties. As a tool, a matrix construction is introduced which might be of independent interest in inverse semigroup theory. Using this construction as well as Ramsey's theorem, we embed a certain kind of inverse monoid into a factorizable monoid of the same kind. As noticed by M. Lawson, this embedding entails that the embedded finite monoids have finite F-unitary cover.

Key concepts: Mathematics, Monoid, Congruence relation, Inverse semigroup, Semigroup, Bicyclic semigroup, Characterization (materials science), Free monoid

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