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.

in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.

In this paper we study the (minus-)generator A p of the C 0-semigroup e A p t on L p (X;) associated with a classical symmetric diiusion form E in L 2 (X;), on a (innnite dimensional) locally convex state space X endowed with a nite diierentiable Borel measure. It is a standard fact that E associates a C 0 sub-Markovian semigroup of contractions on L 2 (X;) and the semigroup interpolates to all...

We present several characterizations, via some weak observability inequalities, on the complete stabilizability for a control system $[A,B]$, i.e., $y'(t)=Ay(t)+Bu(t)$, $t\geq 0$, where $A$ generates $C_0$-semigroup Hilbert space $X$ and $B$ is linear bounded operator from another $U$ to $X$. then extend aforementioned characterizations in two directions: first, unbounded; second, time periodic...

Consider a semigroup action on a set. We derive conditions, in terms of the induced action of the semigroup on {0, 1}-valued probability charges, which ensure that all invariant probability charges are strongly continuous.

A semigroup whose bi-ideals and quasi-ideals coincide is called a -semigroup. The full transformation semigroup on a set X and the semigroup of all linear transformations of a vector space V over a field F into itself are denoted, respectively, by T(X) and LF(V). It is known that every regular semigroup is a -semigroup. Then both T(X) and LF(V) are -semigroups. In 1966, Magill introduced and st...