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On SLA-ideals. (English) Zbl 0840.20065
A semigroup left \(A\)-ideal (SLA-ideal) of a semigroup \(S\) is a subsemigroup \(X\) of \(S\) such that \(sX\cap X\neq\emptyset\) for every \(s\in S\). (SLA-ideals are the same as M. Putcha’s mild ideals [Proc. Am. Math. Soc. 47, 49-52 (1975; Zbl 0307.20036)].) A semigroup is said to be SLA-simple if it has no proper SLA-ideals. The main result of the paper reads as follows: A semigroup has a minimal SLA-ideal if and only if it has a kernel which is a rectangular band of SLA-simple groups; in the commutative case the latter condition reduces to the kernel being a periodic group.

MSC:
20M12 Ideal theory for semigroups
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