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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