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.

In this paper we have introduced fuzzy quasi-ideal and fuzzy left(right, two-sided) ideals in LA-semigroup. We have proved some results related to fuzzy quasi-ideals and fuzzy left(right, two-sided) ideals of an LA-semigroup. Further we characterize an intra-regular LA-semigroup by the properties of their fuzzy ideals.

Rauzy graphs of subshifts are endowed with an automaton structure. For Sturmian subshifts, it is shown that its transition semigroup is the syntactic semigroup of the language recognized by the automaton. A projective limit of the partial semigroups of nonzero regular elements of their transition semigroups is described. If the subshift is minimal, then this projective limit is isomorphic, as a...