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: 111; Downloads: 0 Full text (277,55 KB) This document has many files! More... |
2. A hyperstructural approach to semisimplicityErgül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, original scientific article Abstract: 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. Keywords: direct sum, simple hypermodule, semisimple hypermodule Published in RUNG: 31.01.2024; Views: 637; Downloads: 11 Full text (328,98 KB) This document has many files! More... |
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