Results 21 to 30 of about 117 (89)

r‐Hyperideals and Generalizations of r‐Hyperideals in Krasner Hyperrings

Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022
This paper deals with Krasner hyperrings as an important class of algebraic hyperstructures. We investigate some properties of r‐hyperideals in commutative Krasner hyperrings. Some properties of pr‐hyperideals are also studied. The relation between prime hyperideals and r‐hyperideals is investigated. We show that the image and the inverse image of an r‐
Peng Xu, Melis Bolat, Elif Kaya, Serkan Onar, Bayram Ali Ersoy, Kostaq Hila, Kamal Kumar   +6 more
wiley   +1 more source

A Study on A − I − Γ‐Hyperideals and (m, n) − Γ‐Hyperfilters in Ordered Γ‐Semihypergroups

Discrete Dynamics in Nature and Society, Volume 2021, Issue 1, 2021., 2021
The concept of almost interior Γ‐hyperideals (A − I − Γ‐hyperideals) in ordered Γ‐semihypergroups is a generalization of the concept of interior Γ‐hyperideals (I − Γ‐hyperideals). In this study, the connections between I − Γ‐hyperideals and A − I − Γ‐hyperideals in ordered Γ‐semihypergroups were presented.
Yongsheng Rao, Saeed Kosari, Zehui Shao, Maryam Akhoundi, Saber Omidi, Tien Van Do   +5 more
wiley   +1 more source

About the Normal Projectivity and Injectivity of Krasner Hypermodules

Axioms, 2021
Inspired by the concepts of projective and injective modules in classical algebraic structure theory, in this paper we initiate the study of the chains of hypermodules over a Krasner hyperring R, endowing first the set HomRn(M,N) of all normal ...
Hashem Bordbar, Irina Cristea
doaj   +1 more source

[Retracted] Topological Structures of Lower and Upper Rough Subsets in a Hyperring

Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021
In this paper, we study the connection between topological spaces, hyperrings (semi‐hypergroups), and rough sets. We concentrate here on the topological parts of the lower and upper approximations of hyperideals in hyperrings and semi‐hypergroups. We provide the conditions for the boundary of hyp‐ideals of a hyp‐ring to become the hyp‐ideals of hyp ...
Nabilah Abughazalah, Naveed Yaqoob, Kiran Shahzadi, naeem jan   +3 more
wiley   +1 more source

On Homomorphisms of Krasner Hyperrings

Annals of the Alexandru Ioan Cuza University - Mathematics, 2011
On Homomorphisms of Krasner Hyperrings By a homomorphism from a Krasner hyperring (A, +, ·) into a Krasner hyperring (A', +', ·') we mean a function ƒ: A → A' satisfying ƒ(x + y) ⊆ ƒ(x)+ ƒ(y) and ƒ(x · y) = ƒ(x) ·' ƒ(y) for all ×, y ∈ A. The kernel of ƒ, ker ƒ, is defined by ker ƒ = {x ∈ A | ƒ(x) = 0'} where 0' is the zero of (A', +', ·').
Phanthawimol, W., Punkla, Y., Kwakpatoon, K., Kemprasit, Y.   +3 more
openaire   +1 more source

Regular Parameter Elements and Regular Local Hyperrings

Mathematics, 2021
Inspired by the concept of regular local rings in classical algebra, in this article we initiate the study of the regular parameter elements in a commutative local Noetherian hyperring.
Hashem Bordbar, Irina Cristea
doaj   +1 more source

ON STRONGLY ASSOCIATIVE HYPERRINGS [PDF]

Journal of Algebraic Systems, 2019
This paper generalizes the idea of strongly associative hyperoperation introduced in [7]  to the class of hyperrings. We introduce and investigate hyperrings of type 1, type 2 and SDIS.
Fatemeh Arabpur, Morteza Jafarpour
doaj   +1 more source

On the Borderline of Fields and Hyperfields

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   +1 more source

Fundamental System and Boundary Structure of Topological Krasner Hypermodules [PDF]

Sahand Communications in Mathematical Analysis
In this article, we first define hyperstructures known as Krasner hypermodules. Then, the concept of topological Krasner hypermodules is explored, examining their fundamental propertiesand the notion of continuous mappings that exist between such ...
Azam Zare, Bijan Davvaz
doaj   +1 more source

On d-prime hyperideals of hyperrings [PDF]

Journal of Hyperstructures
For Krasner hyperrings, we study d-prime hyperideals where d is a homo-derivation. Furthermore, we show that every maximal d-hyperideal and d-prime hyperideal is a prime hyperideal of a commutative hyperring.
Maryam Akhoundi, Saber Omidi
doaj   +1 more source