For any group G and any set A, a cellular automaton (CA) is a transformation of the configuration space A G defined via a finite memory set and a local function. Let CA(G; A) be the monoid of all CA over A G. In this paper, we investigate a generalisation of the inverse of a CA from the semigroup-theoretic perspective. An element τ ∈ CA(G; A) is von Neumann regular (or simply regular) if there ...

We show that if A is a stable basis algebra satisfying the distributivity condition, then B is a reduct of an independence algebra A having the same rank. If this rank is finite, then the endomorphism monoid of B is a left order in the endomorphism monoid of A.

The aim of this paper is to investigate whether the class of automaton semigroups is closed under certain semigroup constructions. We prove that the free product of two automaton semigroups that contain left identities is again an automaton semigroup. We also show that the class of automaton semigroups is closed under the combined operation of ‘free product followed by adjoining an identity’. W...

In this paper, the endomorphism monoid of n-prism Pr(n) is explored explicitly. It is shown that Pr(2m + 1) is endomorphism regular for any m ≥ 1 and Pr(2m) is not endomorphism regular for any m ≥ 2. Mathematics Subject Classification: 05C25, 20M20

We propose a new approach to the notion of recognition, which departs from the classical definitions by three specific features. First, it does not rely on automata. Secondly, it applies to any Boolean algebra (BA) of subsets rather than to individual subsets. Thirdly, topology is the key ingredient. We prove the existence of aminimum recognizer in a very general setting which applies in partic...

We define, for any special matching of a finite graded poset, an idempotent, regressive and order preserving function. consider the monoid generated by such functions. call idempotent element this monoid. They are interval retracts. Some them realize kind parabolic map called projections. prove that, in Eulerian posets, image projection, its complement, induced subposets. In Coxeter group, all ...

 Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors.  The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zero  zero-divisors of  $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  In this paper, we bring some results about undirected zero-divisor graph of a monoid ring o...

We develop the K-theory of sets with an action a pointed monoid (or scheme), analogous to modules over ring scheme). In order form localization sequences, we construct quotient category nice regular by Serre subcategory.

Throughout this paper, the ring R is not necessarily with an identity. We denote the set of all idempotents of R by E(R). Also, for a subset X ⊆ R, we denote the right (resp., left) annihilator of X in R by annr(X) (resp., ann (X)). Now, according to Fraser and Nicholson in [5], we call a ring R a left p.p.-ring, in brevity, l.p.p.-ring, if for all x ∈ R, there exists an idempotent e such that ...

Let X∗ be a free monoid over an alphabet X and W be a finite language over X. Let S(W ) be the Rees quotient X∗/I(W ), where I(W ) is the ideal of X∗ consisting of all elements of X∗ that are not subwords of W . Then S(W ) is a finite monoid with zero and is called the discrete syntactic monoid of W . W is called finitely based if the monoid S(W ) is finitely based. In this paper, we give some ...