Abstract We build on the description of left congruences an inverse semigroup in terms kernel and trace due to Petrich Rankin. The notion for a congruence is developed. Various properties are discussed, particular that full subsemigroup both maps onto $$\cap $$ ? -homomorphisms. It shown determined by its ker...

Properties of the category consisting of all objects of the form (X,S, λ) are investigated, where X is a convergence space, S is a commutative semigroup, and λ : X × S → X is a continuous action. A ”generalized quotient” of each object is defined without making the usual assumption that for each fixed g ∈ S, λ(., g) : X → X is an injection. 2000 AMS Classification: 54A20, 54B15, 54B30

We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the C ∗-algebra of the graph. We show that the crossed product by this action is stably isomorphic to the C ∗-algebra of a quotient graph. Our main tool is Laca’s dilation theory for endomorphic actions of Ore semigroups on C ∗-algebras, which embeds such an action in an automorphic ...

A hypertoric variety is a quaternionic analogue of a toric variety. Just as the topology of toric varieties is closely related to the combinatorics of polytopes, the topology of hypertoric varieties interacts richly with the combinatorics of hyperplane arrangements and matroids. Using finite field methods, we obtain combinatorial descriptions of the Betti numbers of hypertoric varieties, both f...

The Abelian Sandpile Model is a diffusion process on graphs, studied, under various names, in statistical physics, theoretical computer science, and algebraic graph theory. The model takes a rooted directed multigraph X ∗, the ambient space, in which the root is accessible from every vertex, and associates with it a commutative monoid M, a commutative semigroup S, and an abelian group G as foll...

The zero-divisor graph of a commutative semigroup with zero is the graph whose vertices are the nonzero zero-divisors of the semigroup, with two distinct vertices adjacent if the product of the corresponding elements is zero. New criteria to identify zerodivisor graphs are derived using both graph-theoretic and algebraic methods. We find the lowest bound on the number of edges necessary to guar...

We study numerical semigroups generated by intervals and solve the following problems related to such semigroups: the membership problem, give an explicit formula for the Frobe-nius number, decide whether the semigroup is a complete intersection and/or symmetric, and computation of the cardi-nality of a (any) minimal presentation of this kind of numerical semigroups. A numerical semigroup is a ...

The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We introduce a new class of regular languages, called the maximally atomic languages, consisting of all languages meeting these bounds. We prove the following result:...