×

zbMATH — the first resource for mathematics

Commutative cancellative semigroups of dimension 1. (Russian) Zbl 0729.20033
For a semigroup S by cd(S) the cohomological dimension of S is denoted. In the paper the following theorem is proved. Theorem. For a commutative cancellative semigroup S \(cd(S)=1\) if and only if S is isomorphic either to the additive group \({\mathbb{Z}}\) of integers or to a subsemigroup of the additive semigroup \({\mathbb{N}}=\{0,1,2,...,n,...\}\). It is noted that in the noncommutative case the situation is more complicated.

MSC:
20M50 Connections of semigroups with homological algebra and category theory
20M14 Commutative semigroups
PDF BibTeX XML Cite