Commutative semigroups that are simple over their endomorphism semirings. (English) Zbl 1260.20082

Summary: Commutative semigroups simple over their endomorphism semirings are investigated. In particular, commutative semigroups having just two fully invariant congruences are classified into five basic types and each of these types is characterized.


20M14 Commutative semigroups
16Y60 Semirings
20M15 Mappings of semigroups
08A30 Subalgebras, congruence relations