Results 41 to 50 of about 117 (89)

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

Exact category of hypermodules

International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006
It is shown, among other things, that the category of hypermodules is an exact category, thus generalizing the classical case.
A. Madanshekaf
wiley   +1 more source

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

New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle.
Matthew Baker, Tong Jin, Oliver Lorscheid   +2 more
wiley   +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

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

A class of hyperrings and hyperfields

International Journal of Mathematics and Mathematical Sciences, Volume 6, Issue 2, Page 307-311, 1983., 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. When the non‐zero elements of a hyperring form a multiplicative group, the hyperring is called a hyperfield, and this ...
Marc Krasner
wiley   +1 more source

Fundamental relation on m-idempotent hyperrings

Open Mathematics, 2017
The γ*-relation defined on a general hyperring R is the smallest strongly regular relation such that the quotient R/γ* is a ring. In this note we consider a particular class of hyperrings, where we define a new equivalence, called εm∗$\varepsilon^{*}_{m}
Norouzi Morteza, Cristea Irina
doaj   +1 more source