Comultiplication on monoids

Martin Arkowitz and Mauricio Gutierrez

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-9

Abstract:

A comultiplication on a monoid S is a homomorphism m : S → S ∗ S (the free product of S with itself) whose composition with each projection is the identity homomorphism. We investigate how the existence of a comultiplication on S restricts the structure of S . We show that a monoid which satisfies the inverse property and has a comultiplication is cancellative and equidivisible. Our main result is that a monoid S which satisfies the inverse property admits a comultiplication if and only if S is the free product of a free monoid and a free group. We call these monoids semi-free and we study different comultiplications on them.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:571812

DOI: 10.1155/S0161171297001099

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