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Green’s relations for the variants of transformation semigroups preserving an equivalence relation. (English) Zbl 1127.20044

The subject of this paper is \(T_E(X)\), the subsemigroup of the full transformation semigroup \(T_X\) of all mappings that respect a given equivalence relation \(E\) of \(X\). Fix \(\theta\) in \(T_E(X)\) and introduce a new semigroup operation \(\circ\) on \(T_E(X)\) by \(f\circ g=f\theta g\); this new semigroup is known as a variant semigroup of \(T_E(X)\). This paper calculates Green’s relations for variants and identifies the regular elements.

MSC:

20M20 Semigroups of transformations, relations, partitions, etc.
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