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Comultiplication on monoids

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  • Martin Arkowitz
  • Mauricio Gutierrez

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.

Suggested Citation

  • Martin Arkowitz & Mauricio Gutierrez, 1997. "Comultiplication on monoids," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:571812
    DOI: 10.1155/S0161171297001099
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