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1.
A characterization of normal injective and normal projective hypermodules
Ergül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, izvirni znanstveni članek

Opis: 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.
Ključne besede: short exact sequence, normal injective hypermodule, normal projective hypermodule
Objavljeno v RUNG: 20.06.2024; Ogledov: 159; Prenosov: 2
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2.
Categorical approach of normal injective and torsionable hypermodules
Hashem Bordbar, 2024, objavljeni povzetek znanstvenega prispevka na konferenci

Opis: 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.
Ključne besede: hypermodules, hyperrings, normal injective, normal projective
Objavljeno v RUNG: 18.06.2024; Ogledov: 170; Prenosov: 0
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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: 1543; Prenosov: 0
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