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One-sided principal ideals in the direct product of two semigroups. (English) Zbl 0810.20043
Author’s summary: A necessary and sufficient condition is given for a principal left ideal \(L(s,t)\) [an \({\mathcal L}\)-class \(L_{(s,t)}\)] in \(S \times T\) to be equal to the direct product of the corresponding principal left ideals \(L(s) \times L(t)\) [\({\mathcal L}\)-classes \(L_ s \times L_ t\)].

MSC:
20M10 General structure theory for semigroups
20M12 Ideal theory for semigroups
20M15 Mappings of semigroups
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