Directed colimits of free commutative semigroups
type: Item
instance of: scholarly article
title: Directed colimits of free commutative semigroups
zbMATH Open document ID: 0358.20067
DOI: 10.1016/0022-4049(76)90007-4
author: Pierre Antoine Grillet
published in: Journal of Pure and Applied Algebra
publication date: 1976-01-01T00:00:00Z
review text: The main results of the paper were announced by the author earlier [Semigroup Forum 1, 162--168 (1970; Zbl 0211.33701); ibid. 1, 249--253 (1970; Zbl 0211.33702)]. He proves that a commutative monoid is a directed colimit of free commutative monoids iff It is cancellative, reduced, and has the strong Riesz interpolation property. A commutative semigroup without identity element is a directed colimit of free semigroups iff \(S\) with identity adjoined is a directed colimit of free monoids. If \(S\) is a cancellative, power-cancellative reduced commutative monoid, then it can be embedded into a directed colimit \(\bar{S}\) of free commutative monoids, so that every homomorphism of \(S\) into a directed colimit of free commutative monoids extends to \(\bar{S}\).
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 3558105
MaRDI profile type: Publication
full work available at URL: 0022-4049(76)90007-4
OpenAlex ID: W2079345429
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description: scientific article; zbMATH DE number 3558105