Related papers: Rings and Fields from Semigroups

We introduce partial group algebras with relations in a purely algebraic framework. Given a group and a set of relations, we define an algebraic partial action and prove that the resulting partial skew group ring is isomorphic to the…

We consider a convenient category of "quadratic" multirings, that allows simple functorial relations with categories associated with abstract quadratic forms theories and shares many good aspects of the theories of Special Groups and of…

We introduce and study an abstract class of semirings, which we call exact semirings, defined by a Hahn-Banach-type separation property on modules. Our motivation comes from the tropical semiring, and in particular a desire to understand…

In this paper, we give an introduction to basic concepts of automaton semigroups. While we must note that this paper does not contain new results, it is focused on extended introduction in the subject and detailed examples.

Consideration of certain properties of group rings and their ideals search

We look at the semigroup generated by a system of heat equations. Applications to testing normality and option pricing are addressed.

In this paper we study numerical semigroups generated by three elements. We give a characterization of pseudo-symmetric numerical semigroups. Also, we will give a simple algorithm to get all the pseudo-symmetric numerical semigroups with…

The notion of locality semigroups was recently introduced with motivation from locality in convex geometry and quantum field theory. We show that there is a natural correspondence between locality sets and quivers which leads to a concrete…

Injective modules play an important role in characterizing different classes of rings (e.g. Noetherian rings, semisimple rings). Some semirings have no non-zero injective semimodules (e.g. the semiring of non-negative integers). In this…

Simple constructions are given for finite semifields that include as special cases both old semifields and recently constructed semifields.

Motivated by situations in which the removal of a zero (a.k.a., an absorbing element) from a semigroup yields a subsemigroup with another zero, sets of quasi-zeros (a.k.a., quasi-absorbing elements) are introduced as well as primitive…

In this paper is proved that the group of automorphisms of semigroup End(P[X]), if P is algebraically closed field, is generated by semi-inner automorphisms.

This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…

The purpose of this paper is to introduce and study a Hom-type generalization of rings. We provide their basic properties and and some key constructions. Furthermore, we consider modules over Hom-rings and characterize the category of…

In this paper we give an algebraic characterization of assemblies in terms of bands of groups. We also consider substructures and homomorphisms of assemblies. We give many examples and counterexamples.

Necessary and sufficient conditions for finite semihypergroups to be built from groups of the same order are established

A flag manifold over a semifield K can be partitioned into "half i-circles" which are orbits of a K-action on that flag manifold. Here i is fixed and it corresponds to a simple reflection in the Weyl group. We prove (for certain K) a…

We study ideal-simple commutative semirings and summarize the results giving their classification, in particular when they are finitely generated. In the principal case of (para)semifields, we then consider their minimal number of…

This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…

For a number field $K$, we extend the notion of the ring class field of an order in $K$ [C. Lv and Y. Deng, SciChina. Math., 2015] to that of an arbitrary number ring in $K$. We give both ideal-theoretic and idele-theoretic description of…