Related papers: Eversible and reversible semigroups and semirings
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…
In this paper, we investigate semirings whose elements are either units or zero-divisors (nilpotents) with many examples. While comparing these semirings with their counterparts in ring theory, we observe that their behavior is different in…
In this paper, we investigate zero-divisor, nilpotent, idempotent, unit, small, and irreducible elements in semiring extensions such as amount, content, and monoid semialgebras. We also introduce new concepts such as the prime avoidance…
In this paper, we investigate the algebraic properties of the expectation semirings which are semiring version of the concept of trivial extension in ring theory. We discuss ideals, primes, maximals and primary ideals of these semirings. We…
A semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. A po-semiring is a semiring equipped with a compatible bounded partial order. In this paper, properties of…
We survey theory developed over the past 10 years of semirings which need not be additively cancellative. The main feature is a specified ``null ideal'' $\mcA_0$ of a semiring $\mcA,$ taking the place of a zero element, which permits…
In the first section of this paper, we introduce the notions of fractional and invertible ideals of semirings and characterize invertible ideals of a semidomain. In section two, we define Pr\"{u}fer semirings and characterize them in terms…
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…
The paper is an overview of recent results on algebraic structures (semigroups, groupoids, algebras, inverse semigroups, and groups) associated with objects with a rich set of partial symmetries. We discuss etale groupoids and inverse…
In this work we prove the undecidability (and $\Sigma^0_1$-completeness) of several theories of semirings with fixed points. The generality of our results stems from recursion theoretic methods, namely the technique of effective…
In this paper we introduce the notion of m-irreducibility that extends the standard concept of irreducibility of a numerical semigroup when the multiplicity is fixed. We analyze the structure of the set of m-irreducible numerical…
In Section 1 of the paper, we prove McCoy's property for the zero-divisors of polynomials in semirings. We also investigate zero-divisors of semimodules and prove that under suitable conditions, the monoid semimodule $M[G]$ has very few…
We investigate ideal-semisimple and congruence-semisimple semirings. We give several new characterizations of such semirings using e-projective and e-injective semimodules. We extend several characterizations of semisimple rings to (not…
The relationship between fuzzy algebras and semirings is explored with fuzzy algebra operators replacing the arithmetic operators of semirings. A new class of fuzzy structures which are similar to semirings is defined. Results of partial…
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…
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…
The structure of categorical at zero semigroups is studied from the point of view their likeness to categories.
In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several…
Let R be a semiring. We say that a non-zero subsemimodule S of an R-semimodule M is second if for each a \in R, we have aS = S or aS = 0. The aim of this paper is to study the notion of second subsemimodules of semimodules over commutative…
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…