Zak Mesyan1,∗, James D. Mitchell2,∗∗, Michał Morayne3,∗∗∗, and Yann H. Péresse2,† 1 Department of Mathematics, University of Colorado, 1420 Austin Bluffs Parkway, Colorado Springs, CO 80918, United States of America 2 Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland 3 Institute of Mathematics and Computer Science, Wrocław University of Technolo...

The variant of a semigroup S with respect to an element a ∈ S, denoted S, is the semigroup with underlying set S and operation ? defined by x ? y = xay for x, y ∈ S. In this article, we study variants T a X of the full transformation semigroup TX on a finite set X. We explore the structure of T a X as well as its subsemigroups Reg(T a X) (consisting of all regular elements) and E X (consisting ...

in the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(s) is the dual of a function algebra.

The paper shows how some semigroup-theory methods can be used in automata problems. The theory of automata is closely connected with the theory of semigroups (or, to be more exact, with the theory of representations of semigroups by transformations). The concept of automaton without outputs is equivalent to the concept of representa­ tion of free semigroup by transformations. If we consider eve...

Abstract We prove that the generator of $$L^2$$ L 2 implementation a KMS-symmetric quantum Markov semigroup can be expressed as square derivation with values in Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups seco...

For a nonempty set X, let T(X) be the total transformation semigroup on X. In this paper, we consider subsemigroups of which are defined by T(X,Y) ={α∈T(X):Xα⊆Y}andS(X,Y)={α∈T(X):Yα⊆Y} where Y is non-empty subset We characterize left regular and right elements both S(X,Y). Moreover, necessary sufficient conditions for S(X,Y) to given. These results then applied determine numbers in finite