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1.
A hyperstructural approach to semisimplicity
Ergül 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: 372; Downloads: 4
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2.
Supplements Related to Normal p-Projective Hypermodules
Burcu Turkmen, Hashem Bordbar, Irina Elena Cristea, 2022, original scientific article

Abstract: 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.
Keywords: direct summand, normal p-projective hypermodule, supplement subhypermodule, small subhypermodule
Published in RUNG: 06.06.2022; Views: 1314; Downloads: 0
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