By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup S in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of Booleannes present in the semilattice of idempotents of ...

In this paper, as a further generalization of ideals, we introduce the notion symmetric bi-interior ideal quasi ideal, bi-ideal and interior semigroup study properties ideals simple semigroup.