Results 51 to 60 of about 3,848 (106)

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 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

Hyper vector spaces over Krasner hyperfields [PDF]

Journal of Algebraic Hyperstructures and Logical Algebras, 2020
In this paper, we study hyper vector spaces over Krasner hyperfields. First, we introduce the notions of linearly independence (dependence) and basis for a hyper vector space. Second, we investigate their properties and prove some results for hyper vector spaces that are similar to that of vector spaces over fields.
M. Al-Tahan, Bijan Davvaz
openaire   +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

On Fuzzy Ordered Hyperideals in Ordered Semihyperrings

Advances in Fuzzy Systems, Volume 2019, Issue 1, 2019., 2019
In this paper, we introduce the concept of fuzzy ordered hyperideals of ordered semihyperrings, which is a generalization of the concept of fuzzy hyperideals of semihyperrings to ordered semihyperring theory, and we investigate its related properties. We show that every fuzzy ordered quasi‐hyperideal is a fuzzy ordered bi‐hyperideal, and, in a regular ...
O. Kazancı, Ş. Yılmaz, B. Davvaz, Antonin Dvorák   +3 more
wiley   +1 more source

δ‐Primary Hyperideals on Commutative Hyperrings

International Journal of Mathematics and Mathematical Sciences, Volume 2017, Issue 1, 2017., 2017
The purpose of this paper is to define the hyperideal expansion. Hyperideal expansion is associated with prime hyperideals and primary hyperideals. Then, we define some of their properties. Prime and primary hyperideals’ numerous results can be extended into expansions.
Elif Ozel Ay, Gürsel Yesilot, Deniz Sonmez, Aloys Krieg   +3 more
wiley   +1 more source

States and Measures on Hyper BCK‐Algebras

Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014
We define the notions of Bosbach states and inf‐Bosbach states on a bounded hyper BCK‐algebra (H, ∘, 0, e) and derive some basic properties of them. We construct a quotient hyper BCK‐algebra via a regular congruence relation. We also define a ∘‐compatibled regular congruence relation θ and a θ‐compatibled inf‐Bosbach state s on (H, ∘, 0,e). By inducing
Xiao-Long Xin, Pu Wang, Baolin Wang
wiley   +1 more source

Associate, Hyperdomainlike, and Presimplifiable Hyperrings

Journal of Mathematics, Volume 2014, Issue 1, 2014., 2014
Based on the works of Axtell et al., Anderson et al., and Ghanem on associate, domainlike, and presimplifiable rings, we introduce new hyperrings called associate, hyperdomainlike, and presimplifiable hyperrings. Some elementary properties of these new hyperrings and their relationships are presented.
Agboola Adesina Abdul Akeem, Davvaz Bijan, Feng Feng   +2 more
wiley   +1 more source

Classical prime subhypermodules and related extensions [PDF]

Categories and General Algebraic Structures with Applications
In this paper, we extend the notion of prime subhypermodulesto $n$-ary classical prime, $n$-ary weakly classical prime and $n$-ary $\phi$-classical prime subhypermodules of an $(m,n)$-hypermodule over a commutative Krasner $(m,n)$-hyperring.
Mahdi Anbarloei
doaj   +1 more source

Note on Isomorphism Theorems of Hyperrings

International Journal of Mathematics and Mathematical Sciences, Volume 2010, Issue 1, 2010., 2010
There are different notions of hyperrings (R, +, ·). In this paper, we extend the isomorphism theorems to hyperrings, where the additions and the multiplications are hyperoperations.
Muthusamy Velrajan, Arjunan Asokkumar, Heinz Gumm   +2 more
wiley   +1 more source