Abstract
AbstractMotivated 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.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
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