Results 31 to 40 of about 140 (71)

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

Some Properties of Multiplicative Hv‐Rings of Polynomials over Multiplicative Hyperrings

Algebra, Volume 2014, Issue 1, 2014., 2014
The set of all polynomials R[x], over a multiplicative hyperring (R, + , ·), form a commutative group with respect to the component‐wise addition (+) of the polynomials. For polynomials f, g in R[x], f*g is a set of polynomials whose (k + 1)th components k∈N∪0 are chosen from the set ∑i+j=kai · bj, where ai and bj are the (i + 1)th and the (j + 1)th ...
Utpal Dasgupta, Andrei V. Kelarev
wiley   +1 more source

On Real Hyperframes [PDF]

Journal of Hyperstructures
The purpose of this paper is to introduce and study hyperframes. Where a frame is a generlization of a basis of a vector space, a hyperframe will act as a generalization of a basis in hypervector space.
Cody Cassiday
doaj   +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

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

Commutative hypergroups associated with a hyperfield

, 2017
Let [Formula: see text] be a commutative hypergroup and [Formula: see text] a discrete commutative hypergroup. In this paper we introduce a commutative hypergroup [Formula: see text] associated with a hyperfield [Formula: see text] of [Formula: see text]
Tatsuya Tsurii, Satoe Yamanaka, Satoshi Kawakami, Herbert Heyer   +3 more
core   +1 more source

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

Rethinking Global Soil Degradation: Drivers, Impacts, and Solutions

Reviews of Geophysics, Volume 63, Issue 4, December 2025.
Abstract The increasing threat of soil degradation presents significant challenges to soil health, especially within agroecosystems that are vital for food security, climate regulation, and economic stability. This growing concern arises from intricate interactions between land use practices and climatic conditions, which, if not addressed, could ...
Nima Shokri, David A. Robinson, Mehdi Afshar, Christine Alewell, Milad Aminzadeh, Emmanuel Arthur, Nils Broothaerts, Grant A. Campbell, Lina Eklund, Surya Gupta, Richard Harper, Amirhossein Hassani, Cathy Hohenegger, Thomas Keller, Maximilian Kiener, Inma Lebron, Kaveh Madani, Tshilidzi Marwala, Francis Matthews, Per Moldrup, Attila Nemes, Panos Panagos, Remus Prăvălie, Matthias C. Rillig, Philipp Saggau, Salome M. S. Shokri‐Kuehni, Pete Smith, Amy Thomas, Lis Wollesen de Jonge, Dani Or   +29 more
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

Field extensions, derivations, and matroids over skew hyperfields [PDF]

, 2018
We show that a field extension $K\subseteq L$ in positive characteristic $p$ and elements $x_e\in L$ for $e\in E$ gives rise to a matroid $M^\sigma$ on ground set $E$ with coefficients in a certain skew hyperfield $L^\sigma$.
Pendavingh, R., Pendavingh, RA Rudi
core   +2 more sources