Results 31 to 40 of about 270 (106)

Hopkins-Levitzki theorem for Krasner hyperrings

Filomat, 2021
In this paper, our aim is to generalize and extend the Hopkins-Levitzki theorem from noncommutative rings to Krasner hyperring. Also, we prove that a Krasner hyperring R is Noetherian if and only if it satisfies the ascending chain conditions of prime hyperideals.
S. Ostadhadi-Dehkordi, K.P. Shum
openaire   +2 more sources

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

Relations on Krasner \((m,n)\)-hyperrings.

European Journal of Combinatorics, 2010
\textit{G. Crombez} [Abh. Math. Semin. Univ. Hamb. 37, 180-199 (1972; Zbl 0247.08001)] generalized the concept of rings to the case of \(n\)-ary operations. Now this concept is extended to \(n\)-ary hyperoperations. Very elementary properties of such hyper-algebras are proved.
Mirvakili, S., Davvaz, B.
openaire   +2 more sources

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

Zariski Topology of (Krasner) Hyperrings

European Journal of Pure and Applied Mathematics
In this paper, we investigate the Zariski topology on the prime spectrum of commutative Krasner hyperrings and explore its interplay with the underlying algebraic structure. We characterize the topological properties of the spectrum, such as connectedness, irreducibility, compactness, and separation axioms, and provide necessary and sufficient ...
Behnam Afshar, Reza Ameri, Madeleine Al-Tahan   +2 more
openaire   +3 more sources