Representations of weakly regular semirings by sections in a presheaf

Javed, Ahsan; Latif, Raja Mohammad; Shabir, Muhammad

doi:10.1080/00927879308824707

Cited by 5 publications

(4 citation statements)

References 15 publications

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“…1.5. Definition: [1]. A non-empty set H is called a canonical hypergroup or simply a hypergroup if the hypergroupoid (H, ·) satisfies the following properties (1) (a · b) · c = a · (b · c) for all a, b , c ∈ H.…”

Section: Introductionmentioning

confidence: 99%

“…A hypergroup is a semihypergroup (H, ·) on which the reproduction axiom is valid, that is a · H = H · a = H, for all a in H. 1.7. Definition: [1]. A hyperring is an algebraic structure (R, +, ·) which satisfies the following axioms:…”

Section: Introductionmentioning

confidence: 99%

“…1.8. Example: [1]. Let (A, +, ·) be a ring and N be a normal subgroup of its multiplicative semigroup.…”

Section: Introductionmentioning

confidence: 99%

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Semihypergroups characterized by (∈ γ, ∈ γ ∨ qδ)-fuzzy hyperideals

Shabir

Mahmood

2015

IFS

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The concept of hypergroup is generalization of group, first was introduced by Marty [9]. This theory had applications to several domains. Marty had applied them to groups, algebraic functions and rational functions. M. Krasner has studied the notion of hyperring in [11]. G.G Massouros and C.G Massouros defined hyperringoids and apply them in generalization of rings in [10]. They also defined fortified hypergroups as a generalization of divisibility in algebraic structures and use them in Automata and Language theory. T. Vougiouklis has defined the representations and fundamental relations in hyperrings in [14,15]. R. Ameri, H. Hedayati defined k-hyperideals in semihyperrings in [2]. B. Davvaz has defined some relations in hyperrings and prove Isomorphism theorems in [7]. The aim of this article is to initiate the study of semihyperrings and characterize it with hyperideals. In this article we defined semihyperrings, hyperideals, prime, semiprime, irreducible, strongly irreducible hyperideals, m-systems, p-systems, i-systems and regular semihyperrings. We also shown that the lattice of irreducible hyperideals of semihyperring R admits the structure of topology, which is called irreducible spectrum topology.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semihypergroups characterized by (∈ γ, ∈ γ ∨ qδ)-fuzzy hyperideals

Shabir

Mahmood

2015

IFS

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“…H. S. Vandiver [28] primarily generated the structure of semirings. J. Ahsan's [2] introduction and characterization of weakly regular semirings was coined in terms of their ideals. D. H. Lehmer [17] was first introduced ternary algebraic structure in 1932, called triplexes.…”

Section: Introductionmentioning

confidence: 99%