Defines slenderness in semigroups, identifying conditions for slender semigroups, highlighting their properties.
We define the concept of slenderness for arbitrary semigroups containing at least one idempotent element, and give necessary and sufficient conditions for semigroups to be slender. We describe the semigroup of all homomorphisms of the direct product of a nonempty family of groups into a slender rectangular abelian group.
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Attila Nagy (2026) studied this question.