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Commutative semigroups with few fully invariant congruences. I. (English) Zbl 1103.20055
Let $$S$$ be a semigroup. A commutative semigroup $$(M,+)$$ equipped with a scalar multiplication $$S\times M\to M$$ is called a (left) $$S$$-semimodule if $$a(x+y)=ax+ay$$ and $$a(bx)=(ab)x$$ for all $$a,b\in S$$ and $$x,y\in M$$. The congruence-free semimodules called simple semimodules are studied.

##### MSC:
 20M14 Commutative semigroups 16Y60 Semirings 08A30 Subalgebras, congruence relations 20M50 Connections of semigroups with homological algebra and category theory
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