Related papers: Endo-prime hyperideals
We introduce primitive hyperideals of a hyperring R and show relations with R itself, and with maximal and prime hyperideals of R. We endow a Jacobson topology on the set of primitive hyperideals of R and study topological properties of the…
In this paper we obtain some statements concerning ideals of polynomials and apply these results in a number of different situations. Among other results, we present new characterizations of $\mathcal{L}_{\infty}$-spaces, Coincidence…
We introduce the concept of protometric and present some properties of protometrics.
This paper investigates the doubly exponential ideal membership property of the Mayr-Meyer ideals from the point of view of their associated primes. A doubly-exponential upper bound on the set of associated primes is proved. In the paper a…
We study zero divisors and minimal prime ideals in semirings of characteristic one. Thereafter we find a counterexample to the most obvious version of primary decomposition, but are able to establish a weaker version. Lastly, we study…
Three notions of associated prime ideals, which are equivalent in the noetherian case but differ in the non notherian case, are discussed. Examples illustrate the scope of the notions.
This work obtains all the right ideals, radicals, congruences and ideals of the affine near-semirings over Brandt semigroups.
We establish the primary decomposition and uniqueness of primary decomposition for k-ideals in commutative Noetherian semirings.
In this paper the concept of extension of a Q-fuzzy ideal in semigroups has been introduced and some important properties have been studied.
We introduce the concept of constructible ideal and we relate this concept with the notion of constructible simplicial complex. Several properties of constructible ideals are studied.
This paper considers graded near-rings over a monoid G as a generalizations of the graded rings over groups, introduce certain innovative graded weakly prime ideals and graded almost prime ideals as a generalizations of graded prime ideals…
The purpose of this note is to introduce primitive ideals of noncommutative semigroups and study some topological aspects of the corresponding structure spaces.
In this paper, the author introduce and study the notion of pre-{\gamma}-I-open sets in ideal topological space.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
An introduction to Hyperbolic Analysis is presented.
Krasner F^{(m,n)}-hyperring were introduced and investigated by Farshi and Davvaz. In this paper, our purpose is to define and characterize three classes of F-hyperideals in a Krasner F^{(m,n)}-hyperring, namely, prime F-hyperideals,…
A classification up to automorphism of the inner ideals of the real finite-dimensional simple Lie algebras is given, jointly with precise descriptions in the case of the exceptional Lie algebras.
We describe first-degree prime ideals of biquadratic extensions in terms of first-degree prime ideals of two underlying quadratic fields. The identification of the prime divisors is given by numerical conditions involving their ideal norms.…
In this paper, the notions of integral closure of hyperrings and hyperideals in a Krasner hyperring $(R, +, \cdot)$ are defined and some basics properties of them are studied. We define also the notion of hypervaluation hyperideals and then…
The aim of this series of papers is to study $z$-ideals of semirings. In this article, we introduce some distinguished classes of $z$-ideals of semirings, which include $z$-prime, $z$-semiprime, $z$-irreducible, and $z$-strongly irreducible…