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Defining relations and 0-modules over a semigroup. (Russian) Zbl 0543.20052
Let S be a semigroup with zero 0. A 0-module over S is an abelian group M with a mapping $$(S/0)\times M\to M$$ satisfying the following conditions for any $$s,t\in S$$ and $$a,b\in M:\quad s(a+b)=sa+sb,\quad s\cdot t\neq 0\Rightarrow s(ta)=(st)a.$$ The author studies a semigroup $$\bar S$$ connected with the category of 0-modules over S and shows how his results can be applied to computing cohomologies of semigroups.
Reviewer: B.M.Schein

##### MSC:
 20M50 Connections of semigroups with homological algebra and category theory
##### Keywords:
category of 0-modules; cohomologies of semigroups