The rank of a commutative cancellative semigroup. (English) Zbl 1076.20049

Cegarra, A. M.; Petrich, M.

Acta Math. Hung. 107, No. 1-2, 71-75 (2005).

Summary: For a commutative cancellative semigroup \(S\), we define the rank of \(S\) intrinsically. This definition implies that the rank of \(S\) equals the usual rank of its group of quotients. We also characterize the rank in terms of embeddability into a rational vector space of the greatest power cancellative image of \(S\).

MSC:

20M14	Commutative semigroups
20M05	Free semigroups, generators and relations, word problems

Keywords:

commutative cancellative semigroups; rank; groups of quotients; power cancellative images