Commutative cancellative semigroups of dimension 1. (Russian) Zbl 0729.20033

Novikov, B. V.

Mat. Zametki 48, No. 1, 148-149 (1990).

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.

Reviewer: V.Fleischer (Tartu)

MSC:

20M50	Connections of semigroups with homological algebra and category theory
20M14	Commutative semigroups

Keywords:

cohomological dimension; commutative cancellative semigroup