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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
.pdf Celotno besedilo (277,55 KB)
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2.
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: 647; Prenosov: 11
.pdf Celotno besedilo (328,98 KB)
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