Torsion Elements and Torsionable Hypermodules
This article is motivated by the recently published studies on divisible hypermodules and falls in the area of hypercompositional algebra. In particular, it focuses on the torsion elements in Krasner hypermodules. First, we define the concept of a torsion element over a hypermodule, and based on it,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/21/4525 |
| _version_ | 1797631577333694464 |
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| author | Hashem Bordbar |
| author_facet | Hashem Bordbar |
| author_sort | Hashem Bordbar |
| collection | DOAJ |
| description | This article is motivated by the recently published studies on divisible hypermodules and falls in the area of hypercompositional algebra. In particular, it focuses on the torsion elements in Krasner hypermodules. First, we define the concept of a torsion element over a hypermodule, and based on it, we introduce a new class of hypermodules, namely the torsionable hypermodule. After investigating some of their fundamental properties, we will show that the class of torsionable hypermodules is a subclass of the class of divisible hypermodules. Finally, we present the relationships between divisible, torsionable, and normal injective hypermodules. |
| first_indexed | 2024-03-11T11:25:32Z |
| format | Article |
| id | doaj.art-9cbb9863851e46dd8a030be19476c0a8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T11:25:32Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9cbb9863851e46dd8a030be19476c0a82023-11-10T15:08:10ZengMDPI AGMathematics2227-73902023-11-011121452510.3390/math11214525Torsion Elements and Torsionable HypermodulesHashem Bordbar0Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, SloveniaThis article is motivated by the recently published studies on divisible hypermodules and falls in the area of hypercompositional algebra. In particular, it focuses on the torsion elements in Krasner hypermodules. First, we define the concept of a torsion element over a hypermodule, and based on it, we introduce a new class of hypermodules, namely the torsionable hypermodule. After investigating some of their fundamental properties, we will show that the class of torsionable hypermodules is a subclass of the class of divisible hypermodules. Finally, we present the relationships between divisible, torsionable, and normal injective hypermodules.https://www.mdpi.com/2227-7390/11/21/4525hypermoduleszero divisorstorsion elementstorsionable hypermodulesnormal injective hypermodules |
| spellingShingle | Hashem Bordbar Torsion Elements and Torsionable Hypermodules Mathematics hypermodules zero divisors torsion elements torsionable hypermodules normal injective hypermodules |
| title | Torsion Elements and Torsionable Hypermodules |
| title_full | Torsion Elements and Torsionable Hypermodules |
| title_fullStr | Torsion Elements and Torsionable Hypermodules |
| title_full_unstemmed | Torsion Elements and Torsionable Hypermodules |
| title_short | Torsion Elements and Torsionable Hypermodules |
| title_sort | torsion elements and torsionable hypermodules |
| topic | hypermodules zero divisors torsion elements torsionable hypermodules normal injective hypermodules |
| url | https://www.mdpi.com/2227-7390/11/21/4525 |
| work_keys_str_mv | AT hashembordbar torsionelementsandtorsionablehypermodules |