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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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