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1.
Categorical approach of normal injective and torsionable hypermodules
Hashem Bordbar, 2024, published scientific conference contribution abstract

Abstract: Inspired by the characterization of injective objects in category theory, our main purpose in this research is to investigate the relationships of di- visible and injective hypermodules with torsion elements and torsionable hypermodules with a category approach. These days, it is extremely tempt- ing to do the research in an Abelian category, so we discuss these topics in an Abelian category. For a Krasner R-hypermodule M, we ex- tend the definition of a zero-divisor element of R to a zero-divisor ele- ment of R over M, and then the definition of divisible R-hypermodule is introduced. Be- sides, the torsion element and torsionable hypermodule are introduced and we show that every torsionable R-hypermodule M is a normal injective, where R is a commutative hyperring.
Keywords: hypermodules, hyperrings, normal injective, normal projective
Published in RUNG: 18.06.2024; Views: 350; Downloads: 0
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2.
Torsion elements and torsionable hypermodules
Hashem Bordbar, 2023, original scientific article

Abstract: This article is motivated by the recently published studies on divisible hypermodules and falls in the area of hypercompositional algebra. In particular, it focuses on the torsion elements in Krasner hypermodules. First, we define the concept of a torsion element over a hypermodule, and based on it, we introduce a new class of hypermodules, namely the torsionable hypermodule. After investigating some of their fundamental properties, we will show that the class of torsionable hypermodules is a subclass of the class of divisible hypermodules. Finally, we present the relationships between divisible, torsionable, and normal injective hypermodules.
Keywords: hypermodules, zero divisors, torsion elements, torsionable hypermodules, normal injective hypermodules
Published in RUNG: 03.11.2023; Views: 940; Downloads: 3
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3.
Regular parameter elements and regular local hyperrings
Hashem Bordbar, Irina Elena Cristea, 2021, original scientific article

Keywords: Krasner hyperring, prime/maximal hyperideal, length of hypermodules, regular local hyperring, parameter elements
Published in RUNG: 27.01.2021; Views: 2731; Downloads: 92
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4.
A note on the support of a hypermodule
Hashem Bordbar, Michal Novak, Irina Elena Cristea, 2020, original scientific article

Keywords: Krasner hyperring, prime/maximal hyperideal, length of hypermodules, annihilator of hypermodules, support of hypermodules
Published in RUNG: 28.02.2019; Views: 3637; Downloads: 0
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