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1.
A hyperstructural approach to semisimplicity
Ergül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, izvirni znanstveni članek

Opis: 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.
Ključne besede: direct sum, simple hypermodule, semisimple hypermodule
Objavljeno v RUNG: 31.01.2024; Ogledov: 508; Prenosov: 6
.pdf Celotno besedilo (328,98 KB)
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2.
Regular local hyperrings and hyperdomains
Hashem Bordbar, Irina Elena Cristea, Sanja Rasovic, 2022, izvirni znanstveni članek

Opis: 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.
Ključne besede: hyperring, hypermodule, vectorialhyperspace, dimension, regularhyperring, regular parameter element, hyperdomain
Objavljeno v RUNG: 27.09.2022; Ogledov: 1152; Prenosov: 21
.pdf Celotno besedilo (258,07 KB)

3.
Supplements Related to Normal p-Projective Hypermodules
Burcu Turkmen, Hashem Bordbar, Irina Elena Cristea, 2022, izvirni znanstveni članek

Opis: In this study, the role of supplements in Krasner hypermodules is examined and related to normal p-projectivity. We prove that the class of supplemented Krasner hypermodules is closed under finite sums and under quotients. Moreover, we give characterizations of finitely generated supplemented and amply supplemented Krasner hypermodules. In the second part of the paper we relate the normal projectivity to direct summands and supplements in Krasner hypermodules.
Ključne besede: direct summand, normal p-projective hypermodule, supplement subhypermodule, small subhypermodule
Objavljeno v RUNG: 06.06.2022; Ogledov: 1412; Prenosov: 0
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4.
Divisible hypermodules
Hashem Bordbar, Irina Elena Cristea, 2022, izvirni znanstveni članek

Ključne besede: normal injective hypermodule, zero divisor, divisible hypermodule, canonical hypergroup
Objavljeno v RUNG: 11.02.2022; Ogledov: 1880; Prenosov: 34
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5.
About the normal projectivity and injectivity of krasner hypermodules
Hashem Bordbar, Irina Elena Cristea, 2021, izvirni znanstveni članek

Ključne besede: R-hypermodule, simple hypermodule, exact chain
Objavljeno v RUNG: 05.05.2021; Ogledov: 1878; Prenosov: 54
URL Povezava na celotno besedilo
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6.
Some open problems in hypercompositional algebra
Irina Elena Cristea, 2020, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: hypergroup, hyperring, hyperfield, hypermodule, dependence relation, fundamental realtion, fuzzy reducibility
Objavljeno v RUNG: 23.06.2020; Ogledov: 2863; Prenosov: 0
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7.
How to define tensor products of hypermodules
Irina Elena Cristea, Sanja Jančić-Rašović, Sohrab Ostadhadi-Dehkordi, 2018, objavljeni znanstveni prispevek na konferenci

Ključne besede: hyperring, hypermodule, tensor product
Objavljeno v RUNG: 11.07.2018; Ogledov: 3255; Prenosov: 0
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8.
A new type of fuzzy subsemihypermodules
Morteza Norouzi, Irina Elena Cristea, 2017, izvirni znanstveni članek

Opis: 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.
Ključne besede: General hypermodule, (∝, ⋐k)-fuzzy subsemihypermodule, (∝, ∝)-fuzzy subsemihypermodule, (∝, qk)-fuzzy subsemihypermodule
Objavljeno v RUNG: 01.03.2017; Ogledov: 3578; Prenosov: 1
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