1. A hyperstructural approach to semisimplicityErgül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, original scientific article Abstract: In this paper, we provide the basic properties of (semi)simple hypermodules. We show that if a hypermodule M is simple, then (End(M), ·) is a group, where End(M) is the set of all normal endomorphisms of M. We prove that every simple hypermodule is normal projective with a zero singular subhypermodule. We also show that the class of semisimple hypermodules is closed under internal direct sums, factor hypermodules, and subhypermodules. In particular, we give a characterization of internal direct sums of subhypermodules of a hypermodule. Keywords: direct sum, simple hypermodule, semisimple hypermodule Published in RUNG: 31.01.2024; Views: 304; Downloads: 4 Full text (328,98 KB) This document has many files! More... |
2. Regular local hyperrings and hyperdomainsHashem Bordbar, Irina Elena Cristea, Sanja Rasovic, 2022, original scientific article Abstract: This paper falls in the area of hypercompositional algebra. In particular, it focuses on the
class of Krasner hyperrings and it studies the regular local hyperrings. These are Krasner hyperrings R with a unique maximal hyperideal M having the dimension equal to the dimension of the vectorial hyperspace M. The aim of the paper is to show that any regular local hyperring is a hyperdomain. M2 For proving this, we make use of the relationship existing between the dimension of the vectorial hyperspaces related to the hyperring R and to the quotient hyperring R = R , where a is an element in M \ M2, and of the regularity of R. Keywords: hyperring, hypermodule, vectorialhyperspace, dimension, regularhyperring, regular parameter element, hyperdomain Published in RUNG: 27.09.2022; Views: 1018; Downloads: 21 Full text (258,07 KB) |
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8. 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: 3424; Downloads: 1 This document has many files! More... |