Results 41 to 50 of about 3,200 (92)

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

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

δ-primary subhypermodules on Krasner hyperrings [PDF]

Categories and General Algebraic Structures with Applications
In this paper, we study commutative Krasner hyperrings with nonzero identity and nonzero unital hypermodules. We introduce a new concept, the $\delta$-primary subhypermodule on Krasner hyperrings.
Kostaq Hila, Elif Kaya, Melis Bolat, Bayram Ersoy, Serkan Onar, Bijan Davvaz   +5 more
doaj   +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 more general framework than the delta-primary hyperideals [PDF]

, 2023
In this paper we aim to study the notion of (t,n)-absorbing delta-semiprimary hyperideal in a Krasner (m,n ...
Anbarloei, Mahdi
core   +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

On topological quotient hyperrings and α*-relation

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
In this research, we first introduce the concept of a topological Krasner hyperring and then proceed to investigate its properties. By applying relative topology to subhyperrings, we analyze the properties associated with them. In other words, the aim is
Zare A., Davvaz B.
doaj   +1 more source