Results 11 to 20 of about 269,304 (111)

Primal hyperideals of multiplicative hyperring [PDF]

Journal of Algebraic Hyperstructures and Logical Algebras, 2021
Summary: In this paper, we introduce the concepts of adjoint, \(\mathrm{n}\)-adjoint of a hyperideals and primal and \(\mathrm{n}\)-primly hyperideals of a commutative multiplicative hyperrings. Many results con-cerning prime, \(\mathrm{n}\)-primly, primary and primal hyperideals of a commutative multiplicative hy-perrings are given, illustrated by ...
Al-Ashker, Mohammed M., ashour, Arwa, Sabouh, Sanna   +2 more
semanticscholar   +12 more sources

On the Borderline of Fields and Hyperfields [PDF]

Mathematics, 2023
The hyperfield came into being due to a mathematical necessity that appeared during the study of the valuation theory of the fields by M. Krasner, who also defined the hyperring, which is related to the hyperfield in the same way as the ring is related ...
Christos G. Massouros, Gerasimos G. Massouros   +1 more
doaj   +5 more sources

Extensions of n-ary prime hyperideals via an n-ary multiplicative subset in a Krasner (m,n)-hyperring [PDF]

Filomat, 2022
Let R be a Krasner (m, n)-hyperring and S be an n-ary multiplicative subset of R. The purpose of this paper is to introduce the notion of n-ary S-prime hyperideals as a new expansion of n-ary prime hyperideals.
M. Anbarloei
semanticscholar   +4 more sources

A class of hyperrings and hyperfields [PDF]

International Journal of Mathematics and Mathematical Sciences, 1983
Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x+y of two elements, x,y, of a hyperring H is, in general, not an element but a subset of H.
Marc Krasner
doaj   +2 more sources

Some Properties of Multiplicative Hv‐Rings of Polynomials over Multiplicative Hyperrings

Algebra, Volume 2014, Issue 1, 2014., 2014
The set of all polynomials R[x], over a multiplicative hyperring (R, + , ·), form a commutative group with respect to the component‐wise addition (+) of the polynomials. For polynomials f, g in R[x], f*g is a set of polynomials whose (k + 1)th components k∈N∪0 are chosen from the set ∑i+j=kai · bj, where ai and bj are the (i + 1)th and the (j + 1)th ...
Utpal Dasgupta, Andrei V. Kelarev
wiley   +2 more sources

On S-2-Prime Hyperideals of Commutative Hyperrings

Mathematics
This paper introduces the notion of S-2-prime hyperideals, providing a unifying generalization of 2-prime and S-prime hyperideals in multiplicative hyperrings.
Elif Tüysüz, Gürsel Yeşilot, Serkan Onar, Sanem Yavuz   +3 more
doaj   +2 more sources

Generalizations of Prime Hyperideals via Hypersystems in Krasner Hyperrings

Axioms
The aim of this study is to investigate generalized prime hyperideals in the framework of Krasner hyperrings. To this end, new classes of hyperideals are introduced and analyzed based on multiplicatively closed properties.
Mehmet Bozdaş, Ummahan Acar
doaj   +2 more sources

n−ABSORBING I−PRIME HYPERIDEALS IN MULTIPLICATIVE HYPERRINGS [PDF]

Journal of Algebraic Systems
In this paper, we define the concept $I-$prime hyperideal in a multiplicative hyperring $R$. A proper hyperideal $P$ of $R$ is an $I-$prime hyperideal if for $a, b \in R$ with $ab \subseteq P-IP$ implies $a \in P$ or $b \in P$.
Ali Abdullah Mena, Ismael Akray
doaj   +2 more sources

Primary hyperideals of multiplicative hyperrings [PDF]

, 2018
In this article, we study prime, primary, C-hyperideals of multiplicative hyperrings in the senseof Rota [14]. Prime hyperideal avodiance lemma was proved in [4]. We mainly study union of primaryhyperideals in hyperring. Among many results in this study we give the primary hyperideal avodiancelemma.
Sevim, Esra Şengelen, Ersoy, Bayram Ali, Davvaz, Bijan   +2 more
openaire   +2 more sources

Graded hyperideals-based graphs on weak graded multiplicative hyperrings

Journal of Algebra and Its Applications
In this paper, we introduce the notion of weak monoid-graded multiplicative hyperrings and present their properties, special the relation to monoid-graded multiplicative hyperrings. We bring forward the concept of an intersection graph of graded hyperideals of monoid-graded multiplicative hyperrings.
Peyman Ghiasvand, Shirin Toghanipour, Mohammad Hamidi   +2 more
openaire   +2 more sources