Laws for generalised interior operations in semigroups
Tim Stokes · Semigroup Forum · 2023
Abstract Motivated by interior operators and by analogous generalisations of closure operators to semigroups in general, we define left, right and two-sided interior operations on a semigroup S in terms of a distinguished set of idempotents E using the natural order. In the left-sided case, we require that for all $$s\in S$$ s ∈ S , there is a largest $$e\in E$$ e ∈ E under the natural order such that $$es=e$$ e s = e . We generalise them using suitable Green-like relations, and characterise the resulting classes of unary and biunary semigroups as quasivarieties or varieties.