Results 51 to 60 of about 310 (116)

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

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

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

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  

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