Results 41 to 50 of about 255 (98)

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

KRASNER TERNARY HYPER FIELDS AND MORE CHARACTERIZATION OF PRIME AND MAXIMAL HYPER IDEALS IN KRASNER TERNARY HYPER RINGS [PDF]

International Journal of Pure and Apllied Mathematics, 2016
In 2010, Davvaz and Mirvakili introduced a new class of hyper structure called an (m,n)-Krasner hyperring, constructed its quotient class where the hyper ideal considered in the said construction is normal, and proved the isomorphism theorems. Recently, Castillo and Vilela investigated the (2,3)-Krasner hyperring called a Krasner ternary hyperring, and
openaire   +1 more source

On the semi‐sub‐hypergroups of a hypergroup

International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 2, Page 293-304, 1991., 1989
In this paper we study some properties of the semi‐sub‐hypergroups and the closed sub‐hypergroups of the hypergroups. We introduce the correlated elements and the fundamental elements and we connect the concept antipodal of the latter with Frattin′s hypergroup. We also present Helly′s Theorem as a corollary of a more general Theorem.
Ch. G. Massouros
wiley   +1 more source

Some Algebraic Classification of Semiregular Hypermodules in Connection to the Radical

Journal of Mathematics, Volume 2024, Issue 1, 2024.
We call a Krasner right S‐hypermodule A regular if each cyclic subhypermodule of A is a direct summand of A, and we also call A semiregular if every finitely generated subhypermodule of A lies above a direct summand of A. In this study, some properties of such hypermodules are achieved.
Yıldız Aydın, Burcu Nişancı Türkmen, Ma Xuanlong   +2 more
wiley   +1 more source

Recent results in hyperring and hyperfield theory

International Journal of Mathematics and Mathematical Sciences, Volume 11, Issue 2, Page 209-220, 1988., 1987
This survey article presents some recent results in the theory of hyperfields and hyperrings, algebraic structures for which the sum of two elements is a subset of the structure. The results in this paper show that these structures cannot always be embedded in the decomposition of an ordinary structure (ring or field) in equivalence classes and that ...
Anastase Nakassis
wiley   +1 more source

A Note on Hypervector Spaces

, 2011
The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence.
Roy, Sanjay, Samanta, T. K.
core   +1 more source

Height of prime hyperideals in Krasner hyperrings

Filomat, 2017
Extending the notion of dimension of a hyperring, we introduce the concept of height of a prime hyperideal of a hyperring, similarly as in ring theory, and we present some basic properties and relations with the dimension notion. In the second part of the article we illustrate some results concerning the height of prime hyperideals in ...
Cristea, Irina Elena, Bordbar, Hashem
openaire   +2 more sources

Methods of constructing hyperfields

International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 4, Page 725-728, 1985., 1983
In this paper we introduce a class of hyperfields which contains non quotient hyperfields. Thus we give a negative answer to the question of whether every hyperfield is isomorphic to a quotient of a field K by some subgroup G of its multiplicative group.
Ch. G. Massouros
wiley   +1 more source

Hyperfield extensions, characteristic one and the Connes-Consani plane connection [PDF]

, 2014
Inspired by a recent paper of Alain Connes and Catherina Consani which connects the geometric theory surrounding the elusive field with one element to sharply transitive group actions on finite and infinite projective spaces ("Singer actions"), we ...
Thas, Koen
core