Results 41 to 50 of about 239 (103)
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 +3 more
wiley +1 more source
Inductive graded rings, hyperfields and quadratic forms [PDF]
Categories and General Algebraic Structures with ApplicationsIn [6] we developed a k-theory for the category of hyperbolic hyperfields (a category that contains a copy of the category of (pre)special groups): this construction extends, simultaneously, Milnor's k-theory ([20]) and Dickmann-Miraglia's k-theory ([13])
Kaique Roberto, Hugo Mariano
doaj +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
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
Generalisations of Tropical Geometry over Hyperfields [PDF]
, 2022 Hyperfields are structures that generalise the notion of a field by way of allowing the addition operation to be multivalued. The aim of this thesis is to examine generalisations of classical theory from algebraic geometry and its combinatorial shadow ...
JAMES MAXWELL
core +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 +2 more
wiley +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
Convex geometry over ordered hyperfields
, 2023 We initiate the study of convex geometry over ordered hyperfields. We define convex sets and halfspaces over ordered hyperfields, presenting structure theorems over hyperfields arising as quotients of fields. We prove hyperfield analogues of Helly, Radon
Smith, Ben, Maxwell, James
core
Commutative hypergroups associated with a hyperfield [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 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] based on [Formula: see text].
Heyer, Herbert +3 more
openaire +3 more sources
Perfect matroids over skew hyperfields
European Journal of CombinatoricsNathan Bowler
exaly +3 more sources