First, we introduce the concept of intuitionistic fuzzy group congruenceand we obtain the characterizations of intuitionistic fuzzy group congruenceson an inverse semigroup and a T^{*}-pure semigroup, respectively. Also,we study some properties of intuitionistic fuzzy group congruence. Next, weintroduce the notion of intuitionistic fuzzy semilattice congruence and we givethe characterization of...

Let (T∗t) be a predual quantum Markov semigroup acting on the full 2× 2-matrix algebra and having an absorbing pure state. We prove that for any initial state ω, the net of orthogonal measures representing the net of states (T∗t(ω)) satisfies a large deviation principle in the pure state space, with a rate function given in terms of the generator, and which does not depend on ω. This implies th...

Let (B, λt, ψ) be a C-dynamical system where (λt : t ∈ IT+) be a semigroup of injective endomorphism and ψ be an (λt) invariant state on the C ∗ subalgebra B and IT+ is either non-negative integers or real numbers. The central aim of this exposition is to find a useful criteria for the inductive limit state B →t B canonically associated with ψ to be pure. We achieve this by exploring the minima...

We call (T (t))t≥0 an abstract delay semigroup. This notion is introduced in more detail in Section 2. The semigroup thus obtained is rarely a contraction semigroup. In this paper we will show that under very mild conditions, we may change the inner product on E into an equivalent inner product, such that the delay semigroup becomes a (generalized) contraction semigroup. A contraction semigroup...

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...

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...

Let T X be the full transformation semigroup on the setX and let T X,Y {α ∈ T X : Xα ⊆ Y}. Then T X,Y is a sub-semigroup of T X determined by a nonempty subset Y of X. In this paper, we give a necessary and sufficient condition for T X,Y to be regular. In the case that T X,Y is not regular, the largest regular sub-semigroup is obtained and this sub-semigroup is shown to determine the Green’s re...

Quasi-ideals were introduced by Otto Steinfeld [43] as those non-empty subsets Q of a semigroup T satisfying QTD TQ c Q. When T is regular they are precisely the subsets Q of T which satisfy QTQ = Q ([43, Theorem 9.3]). There are many examples of quasi-ideals in regular semigroup theory. We list below some of the most important: • Every subsemigroup of the form eSe (where e is an idempotent) is...

We study asymptotic behavior of a Markov semigroup on a von-Neumann algebra by exploring a maximal von-Neumann subalgebra where the Markov semigroup is an automorphism. This enables us to prove that strong mixing is equivalent to ergodic property for continuous time Markov semigroup on a type-I von-Neumann algebra with center completely atomic. For discrete time dynamics we prove that an aperio...

In this paper we investigate some properties of congruences on ternary semigroups. We also define the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a relation R on T. Furthermore we study the lattice of congruences on a ternary semigroup and we show that this lattice is not generally modular...