Regular monoids generated by two galois connections |
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Authors: | Martin Skorsky |
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Affiliation: | (1) Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstr. 7, D-6100 Darmstadt, Federal Republic of Germany |
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Abstract: | Consider a Galois connection (α, α) on an ordered setP and a Galois connection (β, β) on the dually ordered set . Arbitrary compositions of these Galois connections form a monoid. In this paper we will examine this monoid. First we prove that it is a regular monoid and then we construct two special Galois connectionsa andb such that every monoid of the above type is a homomorphic image of the monoid generated bya andb, and we give a solution of the word problem of the latter monoid. |
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