Cegarra, Antonio M.; Petrich, Mario Commutative cancellative semigroups of finite rank. (English) Zbl 1070.20068 Period. Math. Hung. 49, No. 2, 35-44 (2004). Summary: The rank of a commutative cancellative semigroup \(S\) is the cardinality of a maximal independent subset of \(S\). Commutative cancellative semigroups of finite rank are subarchimedean and thus admit a Tamura-like representation. We characterize these semigroups in several ways and provide structure theorems in terms of a construction akin to the one devised by T. Tamura for \(\mathfrak N\)-semigroups. MSC: 20M14 Commutative semigroups 20M05 Free semigroups, generators and relations, word problems Keywords:commutative cancellative semigroups; finite rank semigroups; Archimedean components PDF BibTeX XML Cite \textit{A. M. Cegarra} and \textit{M. Petrich}, Period. Math. Hung. 49, No. 2, 35--44 (2004; Zbl 1070.20068) Full Text: DOI References: [1] A. M. Cegarra and M. Petrich, The rank of a commutative cancellative semigroup, Acta Math. Hung., (to appear). · Zbl 1076.20049 [2] A. M. Cegarra and M. Petrich, Structure of commutative cancellative subarchimedean semigroups, Bull. Belg. Math. Soc-Sim., (to appear). · Zbl 1132.20037 [3] A. M. Cegarra and M. Petrich, Commutative cancellative semigroups and rational vector spaces, Boll. Unione Mat. Ital., (to appear). · Zbl 1147.20317 [4] J. L. Clarke, A study of commutative cancellative idempotent-free semigroups, Doctoral thesis, Univ. of California, Davis, 1980. [5] P. A. Grillet, Semigroups, An introduction to structure theory, Dekker, NewYork, 1995. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.