1. A characterization of normal injective and normal projective hypermodulesErgül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, original scientific article Abstract: This study is motivated by the recently published papers on normal injective and normal
projective hypermodules. We provide a new characterization of the normal injective and normal
projective hypermodules by using the splitting of the short exact sequences of hypermodules. After presenting some of their fundamental properties, we show that if a hypermodule is normal projective, then every exact sequence ending with it is splitting. Moreover, if a hypermodule is a normal injective, then every exact sequence starting with it is splitting as well. Finally, we investigate the relationships between semisimple, simple, normal injective, and normal projective hypermodules.
Keywords: short exact sequence, normal injective hypermodule, normal projective hypermodule
Published in RUNG: 20.06.2024; Views: 159; Downloads: 2
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2. Categorical approach of normal injective and torsionable hypermodulesHashem 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: 170; Downloads: 0
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3. Torsion elements and torsionable hypermodulesHashem 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: 821; Downloads: 3
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