In this paper, we introduce the notion of (i-v) fuzzy (weakly) completely regular subsemigroup of a semigroup S and study their different properties. We show that every (i-v) fuzzy completely regular subsemigroup of a semigroup S is a union of (i-v) fuzzy subgroups of S. We also characterize (i-v) fuzzy completely regular subsemigroup by (i-v) fuzzy semilattice of (i-v) fuzzy subgroups. 2010 AM...

For a regular biordered set E, the notion of E-diagram and the associated regular semigroup was introduced in our previous paper (1995). Given a regular biordered set E, an E-diagram in a category C is a collection of objects, indexed by the elements of E and morphisms of C satisfying certain compatibility conditions. With such an E-diagram A we associate a regular semigroup RegE(A) having E as...

We consider random walks on idempotent semigroups, called Left Regular Bands, satisfying the relation xyx = xy for any two elements x and y of the semigroup. We give an alternating upper bound for the total variation distance of a random walk on a Left Regular Band semigroup, improving the previous bound by Brown and Diaconis.

The concepts of (λ ,μ)−fuzzy subsemigroup and various (λ ,μ)−fuzzy ideals of a semigroup were introduced by generalizing (∈,∈∨q)−fuzzy subsemigroup and (∈,∈∨q)−fuzzy ideal. The regular semigroup was characterized by the properties of the middle parts of various (λ ,μ)−fuzzy ideals, and several equivalence conditions of regular semigroups were obtained.

In this paper, it is shown that the value semigroup of a prime divisor of the second kind on a 2-dimensional regular local ring is symmetric. Further, a necessary and sufficient condition for two prime divisors of the second kind on a 2-dimensional regular local ring to have the same value semigroup is obtained.