We prove that there is a correspondence between self-similar group actions and the class of left cancellative right hereditary monoids satisfying the dedekind height property. The monoids in question turn out to be coextensive with the Zappa-Szép products of free monoids and groups, and the ideal structure of the monoid reflects properties of the group action. These monoids can also be viewed a...

We develop an effective and natural approach to interpret any semigroup admitting a special language of greedy normal forms as an automaton semigroup, namely the semigroup generated by a Mealy automaton encoding the behaviour of such a language of greedy normal forms under one-sided multiplication. The framework embraces many of the well-known classes of (automatic) semigroups: free semigroups,...

We obtain a complete structural characterization of Cohn-Leavitt algebras over no-exit objects as graded involutive algebras. Corollaries of this result include graph-theoretic conditions characterizing when a Leavitt path algebra is a directed union of (graded) matricial algebras over the underlying field and over the algebra of Laurent polynomials and when the monoid of isomorphism classes of...

For a monoid M , we introduce linear M-Armendariz rings, which are generalization of M-Armendariz rings and linear Armendariz rings; and investigate their properties. Every reduced ring is linear M-Armendariz, for any unique product monoid. We show that if M be a monoid and R be a right ore ring with classical right quotient ring Q. Then R is linear M-Armendariz if and only if Q is linear M-Arm...

Clifford and Preston (1961) showed several important characterizations of right groups. It was shown in Roy and So (1998) that, among topological semigroups, compact right simple or left cancellative semigroups are in fact right groups, and the closure of a right simple subsemigroup of a compact semigroup is always a right subgroup. In this paper, it is shown that such results can be generalize...

A family of subsets of an n-set is 2-cancellative if for every four-tuple {A, B, C, D} of its members A ∪B ∪C = A ∪B ∪D implies C = D. This generalizes the concept of cancellative set families, defined by the property that A ∪B 6= A ∪C for A, B, C all different. The asymptotics of the maximum size of cancellative families of subsets of an n-set is known, (Tolhuizen [7]). We provide a new upper ...

In this paper, we study factorizations in the additive monoids of positive algebraic valuations N0[α] semiring polynomials N0[X] using a methodology introduced by D. Anderson, F. and M. Zafrullah 1990. A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. We begin determining when atomic, give an explicit description its set An finite factorizati...

Let M be a numerical monoid (i.e., an additive submonoid of N0) with minimal generating set 〈n1, . . . , nt〉. For m ∈ M , if m = Pt i=1 xini, then Pt i=1 xi is called a factorization length of m. We denote by L(m) = {m1, . . . , mk} (where mi < mi+1 for each 1 ≤ i < k) the set of all possible factorization lengths of m. The Delta set of m is defined by ∆(m) = {mi+1 −mi | 1 ≤ i < k } and the Del...

In this paper, some categorical properties of the category ${bf Cpo}_{{bf Act}text{-}S}$ of all {cpo $S$-acts}, cpo's equipped with actions of a monoid $S$ on them, and strict continuous action-preserving maps between them is considered. In particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. Also, we show that the forgetful functor from...