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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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