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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.16332 |
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| _version_ | 1866914811821948928 |
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| author | Uçar, Zeynep Yılmaz Ersoy, Bayram Ali Tekir, Ünsal Çelikel, Ece Yetkin Onar, Serkan |
| author_facet | Uçar, Zeynep Yılmaz Ersoy, Bayram Ali Tekir, Ünsal Çelikel, Ece Yetkin Onar, Serkan |
| contents | In this paper, all rings are commutative with nonzero identity. Let M be an R-module. We introduce the concept of phi classical 1-absorbing prime submodules. A proper submodule N of M is a phi classical 1-absorbing prime submodule if whenever non units a, b, c belongs to R and m belongs to M with abcm belongs to N and does not belong to phi(N), then abm belongs to N or cm belongs to N. Many properties and characterizations of phi classical 1-absorbing prime submodules are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phi Classical 1-Absorbing Prime Submodule Uçar, Zeynep Yılmaz Ersoy, Bayram Ali Tekir, Ünsal Çelikel, Ece Yetkin Onar, Serkan Rings and Algebras 13A15, 13C05, 13C60 In this paper, all rings are commutative with nonzero identity. Let M be an R-module. We introduce the concept of phi classical 1-absorbing prime submodules. A proper submodule N of M is a phi classical 1-absorbing prime submodule if whenever non units a, b, c belongs to R and m belongs to M with abcm belongs to N and does not belong to phi(N), then abm belongs to N or cm belongs to N. Many properties and characterizations of phi classical 1-absorbing prime submodules are given. |
| title | Phi Classical 1-Absorbing Prime Submodule |
| topic | Rings and Algebras 13A15, 13C05, 13C60 |
| url | https://arxiv.org/abs/2405.16332 |