In this paper, we give some characterizations of intraregular semigroups by the properties of their (∈,∈ ∨qk)-fuzzy right ideals, (∈,∈ ∨qk)-fuzzy left ideals, (∈,∈ ∨qk)-fuzzy interior ideals, (∈,∈ ∨qk)fuzzy bi-ideals and (∈,∈ ∨qk)-fuzzy generalized bi-ideals. 2010 AMS Classification: 03E72, 20M12

We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine explicitly the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer seq...

This paper studies automatic structures for subsemigroups of Baumslag–Solitar semigroups (that is, semigroups presented by ⟨x, y | (yx, xy)⟩ where m,n ∈ N). A geometric argument (a rarity in the field of automatic semigroups) is used to show that if m > n, all of the finitely generated subsemigroups of this semigroup are [right-] automatic. If m < n, all of its finitely generated subsemigroups ...

This paper makes a comprehensive survey of results relating to finite Rees index for semigroups. In particular, we survey of the state of knowledge on whether various finiteness properties (such as finite generation, finite presentability, automaticity, and hopficity) are inherited by finite Rees index subsemigroups and extensions. We survey other properties that are invariant under passing to ...

Let J be the ideal of vertex covers of a graph G. We give a graph theoretical characterization of the minimal generators of the symbolic Rees algebra of J . If G is perfect, it is shown that the Rees algebra of J is normal and we compute the irreducible representation of the Rees cone of J in terms of cliques. Then we prove that if G is perfect and unmixed, then the Rees algebra of J is a Goren...

A formal mathematical presentation of various algebraic properties of rule 90 elementary one-dimensional cellular automata (CA) with null boundary conditions is given. The CA global rule transition matrix is given and its characteristic polynomial is formally obtained. Mathematical relationships between the CA register lengths and the orders of the corresponding group or semigroup algebraic str...

We develop some new topological tools to study maximal subgroups of free idempotent generated semigroups. As an application, we show that the rank 1 component of the free idempotent generated semigroup of the biordered set of a full matrix monoid of size n×n,n > 2 over a division ring Q has maximal subgroup isomorphic to the multiplicative subgroup of Q.

Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of the Rees algebra of I in terms of an Ehrhart ring. We introduce the basis Rees cone of a matroid (or a polymatroid) and study their facets. Some application...

With the exploitation of rare earth ore, more and more REEs came into groundwater. This was a waste of resources and could be harmful to the organisms. This study aimed to find an efficient adsorption material to mitigate the above issue. Through doping sodium alginate (SA) with poly-γ-glutamate (PGA), an immobilized gel particle material was produced. The composite exhibited excellent capacity...

In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.