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Search Results (4)

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Keywords = normal projective hypermodule

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11 pages, 268 KB  
Article
A Characterization of Normal Injective and Normal Projective Hypermodules
by Ergül Türkmen, Burcu Nİşancı Türkmen and Hashem Bordbar
Axioms 2024, 13(6), 410; https://doi.org/10.3390/axioms13060410 - 18 Jun 2024
Cited by 1 | Viewed by 1491
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 [...] Read more.
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 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. Full article
(This article belongs to the Section Algebra and Number Theory)
16 pages, 317 KB  
Article
A Hyperstructural Approach to Semisimplicity
by Ergül Türkmen, Burcu Nİşancı Türkmen and Hashem Bordbar
Axioms 2024, 13(2), 81; https://doi.org/10.3390/axioms13020081 - 25 Jan 2024
Cited by 4 | Viewed by 1705
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 [...] Read more.
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. Full article
(This article belongs to the Section Algebra and Number Theory)
15 pages, 313 KB  
Article
Supplements Related to Normal π-Projective Hypermodules
by Burcu Nişancı Türkmen, Hashem Bordbar and Irina Cristea
Mathematics 2022, 10(11), 1945; https://doi.org/10.3390/math10111945 - 6 Jun 2022
Cited by 5 | Viewed by 1913
Abstract
In this study, the role of supplements in Krasner hypermodules is examined and related to normal π-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 [...] Read more.
In this study, the role of supplements in Krasner hypermodules is examined and related to normal π-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. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
15 pages, 346 KB  
Article
About the Normal Projectivity and Injectivity of Krasner Hypermodules
by Hashem Bordbar and Irina Cristea
Axioms 2021, 10(2), 83; https://doi.org/10.3390/axioms10020083 - 4 May 2021
Cited by 10 | Viewed by 2591
Abstract
Inspired by the concepts of projective and injective modules in classical algebraic structure theory, in this paper we initiate the study of the chains of hypermodules over a Krasner hyperring R, endowing first the set [...] Read more.
Inspired by the concepts of projective and injective modules in classical algebraic structure theory, in this paper we initiate the study of the chains of hypermodules over a Krasner hyperring R, endowing first the set HomRn(M,N) of all normal homomorphisms between two R-hypermodules M and N with a structure of R-hypermodule. Then, our study focuses on the concepts of normal injectivity and projectivity of hypermodules over a Krasner hyperring R, characterizing them by the mean of chains of R-hypermodules. Full article
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