期刊名称:International Journal of Mathematics and Mathematical Sciences
印刷版ISSN:0161-1712
电子版ISSN:1687-0425
出版年度:1997
卷号:20
DOI:10.1155/S0161171297001099
出版社:Hindawi Publishing Corporation
摘要: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.