Related papers: The endomorphism semiring of a commutative inverse…
The partial automorphism monoid of an inverse semigroup is an inverse monoid consisting of all isomorphisms between its inverse subsemigroups. We prove that a tightly connected fundamental inverse semigroup $S$ with no isolated nontrivial…
The set of all subsets of any inverse semigroup forms an involution semiring under set-theoretical union and element-wise multiplication and inversion. We find structural conditions on a finite inverse semigroup guaranteeing that neither…
We investigate endomorphism semirings of a finite semilattice with one least element and one greatest element such that all the other elements form an antichain. We construct some new finite simple semirings. Keywords: endomorphism…
Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…
Commutative semirings with divisible additive semigroup are studied. We show that an additively divisible commutative semiring is idempotent, provided that it is finitely generated and torsion. In case that a one-generated additively…
Idempotents yield much insight in the structure of finite semigroups and semirings. In this article, we obtain some results on (multiplicatively) idempotents of the endomorphism semiring of a finite chain. We prove that the set of all…
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…
It is an easy observation that every residuated lattice is in fact a semiring because multiplication distributes over join and the other axioms of a semiring are satisfied trivially. This semiring is commutative, idempotent and simple. The…
We introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this inverse semigroup is isomorphic to the group of inner…
The purpose of this paper is to study the generalization of inverse semigroups (without order). An ordered semigroup S is called an inverse ordered semigroup if for every a 2 S, any two inverses of a are H-related. We prove that an ordered…
In this paper we prove that every automorphism of the semigroup of invertible matrices with nonnegative elements over a linearly oredered associative ring on some specially defined subgroup concides with the composition of an inner…
The 5-element Brandt semigroup $B_2$ admits the structure of a naturally semilattice-ordered inverse semigroup, thus becoming an additively idempotent semiring with the operation of taking greatest lower bounds as the semiring addition. For…
Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid. We…
A simple observation, showing that every groupoid becomes an inverse semigroup after adding one element. In such inverse semigroups all idempotents are mutually orthogonal. This fact implies that every C*-algebra of a discrete groupoid is a…
We study the Finite Basis Problem for finite additively idempotent semirings whose multiplicative reducts are inverse semigroups. In particular, we show that each additively idempotent semiring whose multiplicative reduct is a nontrivial…
We prove that a semiring multiplicatively generated by its idempotents is commutative and Boolean, if every idempotent in the semiring has an orthogonal complement. We prove that a semiring additively generated by its idempotents is…
Using the classification and description of the structure of bisimple monogenic orthodox semigroups obtained in \cite{key10}, we prove that every bisimple orthodox semigroup generated by a pair of mutually inverse elements of infinite order…
The 6-element Brandt monoid $B_2^1$ admits a unique addition under which it becomes an additively idempotent semiring. We show that this addition is a term operation of $B_2^1$ as an inverse semigroup. As a consequence, we exhibit an easy…
In this paper, among other results, there are described (complete) simple - simultaneously ideal- and congruence-simple - endomorphism semirings of (complete) idempotent commutative monoids; it is shown that the concepts of simpleness,…
Consider an algebraic semigroup $S$ and its closed subscheme of idempotents, $E(S)$. When $S$ is commutative, we show that $E(S)$ is finite and reduced; if in addition $S$ is irreducible, then $E(S)$ is contained in a smallest closed…