81. HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGSHashem Bordbar, Irina Elena Cristea, Michal Novak, 2017, original scientific article Abstract: Inspired by the classical concept of height of a prime ideal in a ring, we proposed in a precedent paper the notion of height of a prime hyperideal in a Krasner hyperring. In this note we first generalize some results concerning the height of a prime hyperideal in a Noetherian Krasner hyperring, with the intent to extend this definition to the case of a general hyperideal in a such hyperring. The main results in this note show that, in a commutative Noetherian Krasner hyperring, the height of a minimal prime hyperideal over a proper hyperideal generated by n elements is less than or equal to n, the converse of this claim being also true. Based on this result, it can be proved that the height of such a prime hyperideal is limited by the height of a corresponding quotient hyperideal.
Keywords: Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal
Published in RUNG: 01.06.2017; Views: 4574; Downloads: 0
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82. A new type of fuzzy subsemihypermodulesMorteza Norouzi, Irina Elena Cristea, 2017, original scientific article Abstract: In this paper, combining the notions of “belongingness” and “quasi coincidence” of fuzzy points and fuzzy subsets, a new type of fuzzy subsemihypermodules, namely (∝, ⋐k)-fuzzy subsemihypermodules of general hypermodules, is introduced and characterized, using the “max” operator. Their properties and connections with other (α, β)-fuzzy subsemihypermodules are investigated.
Keywords: General hypermodule, (∝, ⋐k)-fuzzy subsemihypermodule, (∝, ∝)-fuzzy subsemihypermodule, (∝, qk)-fuzzy subsemihypermodule
Published in RUNG: 01.03.2017; Views: 3547; Downloads: 1
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83. Fechner, Zywilla (D-ULM-MFN) ; Szekelyhidi, Laszlo (H-LAJO-IM) Sine functions on hypergroups.(English summary) Arch. Math. (Basel) 106 (2016), no. 4, 371 - 382.Irina Elena Cristea, 2017, review, book review, critique Keywords: sine function, cosine function, locally compact hypergroup, functional equations on hypergroups
Published in RUNG: 27.02.2017; Views: 4241; Downloads: 0
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89. Fuzzy Subhypergroups DegreeIrina Elena Cristea, 2016, original scientific article Abstract: In this paper we define the degree to which a fuzzy subset on a hypergroup is a fuzzy subhypergroup by means of the residuate sets, constructed using the minimum t-norm. We give also some properties of this new index connected with the intersection of a family of fuzzy subhypergroups, and respectively with the homomorphic image/preimage of a fuzzy subset. We conclude with addressing new problems related with intuitionistic fuzzy subhypergroups and fuzzy subpolygroups in the framework of our discussion.
Keywords: Fuzzy set, fuzzy subhypergroup, residuate set, t-norm
Published in RUNG: 24.06.2016; Views: 4330; Downloads: 0
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