Distance-regular graphs have been a key concept in Algebraic Combinatorics and have given place to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study ‘almost distance-regular graphs’. We use this name informally for graphs that share some regularity properties that are related to distance in the ...

let $mathcal{a}$ be a banach algebra with bai and $e$ be an introverted subspace of $mathcal{a'}$.in this paper we study the quotient arens regularity of $mathcal{a}$ with respect to $e$ and prove that the group algebra $l^1(g)$ for a locally compact group $g$, is quotient arens regular with respect to certain introverted subspace $e$ of $l^infty(g)$.some related result are given as well.

This paper studies rr-, lr-, rl-, and ll-automatic structures for finitely generated submonoids of monoids presented by confluent rewriting system that are either finite and special or regular andmonadic. A new technique is developed that uses an automaton to ‘translate’ betweenwords in the original rewriting system andwords over the generators for the submonoid. This is applied to show that th...

Margolis, S.W. and J.E. Pin, New results on the conjecture of Rhodes and on the topological conjecture, Journal of Pure and Applied Algebra 80 (1992) 305-313. The Conjecture of Rhodes, originally called the ‘type II conjecture’ by Rhodes, gives an algorithm to compute the kernel of a finite semigroup. This conjecture has numerous important consequences and is one of the most attractive problems...

In this note we will show that the dilation result obtained for fractional skew monoid rings, in the case of a cancellative left Ore monoid S acting on a unital ring A by corner isomorphisms, holds in full generality. We apply this result to the context of semigroup C∗-crossed products.

For integers a and b, 0 ≤ a ≤ b, an [a, b]-graph G satisfies a ≤ deg(x,G) ≤ b for every vertex x of G, and an [a, b]-factor is a spanning subgraph F such that a ≤ deg(x, F ) ≤ b for every vertex x of F . An [a, b]-factor is almost-regular if b = a+1. A graph is [a, b]-factorable if its edges can be decomposed into [a, b]-factors. When both k and t are positive integers and s is a nonnegative in...

Abstract We describe how one can explicitly obtain all atoms of an arbitrary root-closed monoid, whose quotient group is isomorphic to $$\mathbb {Z}^2$$ Z2 . For this purpose, we solve task for three special types such monoids in Theorems 5 and 6, then ...

We generalize to eventually regular (or ‘π-regular’) semigroups the study of the lattice of full regular subsemigroups of a regular semigroup, which has its most complete exposition in the case of inverse semigroups. By means of a judicious definition, it is shown that the full eventually regular subsemigroups of such a semigroup form a complete lattice LF , which projects onto the lattices of ...

In Ufnarovski (1989), the concept of automaton algebras is introduced. These are quotients of the non-commutative polynomial ring where the defining ideal allows some Gröbner basis with a regular set of leading words. However, nothing is reflected concerning the whole structure of the Gröbner basis (except of course for monomial algebras). In this paper we introduce the concept of regular Gröbn...