Results 11 to 19 of about 25 (19)
r‐Hyperideals and Generalizations of r‐Hyperideals in Krasner Hyperrings
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 This paper deals with Krasner hyperrings as an important class of algebraic hyperstructures. We investigate some properties of r‐hyperideals in commutative Krasner hyperrings. Some properties of pr‐hyperideals are also studied. The relation between prime hyperideals and r‐hyperideals is investigated. We show that the image and the inverse image of an r‐
Peng Xu +6 more
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A Study on A − I − Γ‐Hyperideals and (m, n) − Γ‐Hyperfilters in Ordered Γ‐Semihypergroups
Discrete Dynamics in Nature and Society, Volume 2021, Issue 1, 2021., 2021 The concept of almost interior Γ‐hyperideals (A − I − Γ‐hyperideals) in ordered Γ‐semihypergroups is a generalization of the concept of interior Γ‐hyperideals (I − Γ‐hyperideals). In this study, the connections between I − Γ‐hyperideals and A − I − Γ‐hyperideals in ordered Γ‐semihypergroups were presented.
Yongsheng Rao +5 more
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[Retracted] Topological Structures of Lower and Upper Rough Subsets in a Hyperring
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 In this paper, we study the connection between topological spaces, hyperrings (semi‐hypergroups), and rough sets. We concentrate here on the topological parts of the lower and upper approximations of hyperideals in hyperrings and semi‐hypergroups. We provide the conditions for the boundary of hyp‐ideals of a hyp‐ring to become the hyp‐ideals of hyp ...
Nabilah Abughazalah +3 more
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On Fuzzy Ordered Hyperideals in Ordered Semihyperrings
Advances in Fuzzy Systems, Volume 2019, Issue 1, 2019., 2019 In this paper, we introduce the concept of fuzzy ordered hyperideals of ordered semihyperrings, which is a generalization of the concept of fuzzy hyperideals of semihyperrings to ordered semihyperring theory, and we investigate its related properties. We show that every fuzzy ordered quasi‐hyperideal is a fuzzy ordered bi‐hyperideal, and, in a regular ...
O. Kazancı +3 more
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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
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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
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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
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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
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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 +2 more
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