On hyperideals of Krasner hyperrings based on derived unitary rings
In this paper first, we introduce and analyze the strongly regular relations $\lambda^*_{e}$ and $\Lambda^*_{e}$ on a hyperring such that the derived quotient ring is unitary and unitary commutative, respectively. Next, we define and study the notion of $\lambda_e$-parts in a hyperring and characte...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2022-11-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_3280_e7c505906e6c975953a26e9569f6a5a5.pdf |
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| author | Seyed Shahin Mousavi Morteza Jafarpour Hojat Babaei Irina Cristea |
| author_facet | Seyed Shahin Mousavi Morteza Jafarpour Hojat Babaei Irina Cristea |
| author_sort | Seyed Shahin Mousavi |
| collection | DOAJ |
| description | In this paper first, we introduce and analyze the strongly regular relations $\lambda^*_{e}$ and $\Lambda^*_{e}$ on a hyperring such that the derived quotient ring is unitary and unitary commutative, respectively. Next, we define and study the notion of $\lambda_e$-parts in a hyperring and characterize the $\lambda_e$-parts in a $\lambda_e$-strong hyperring $R$. Finally, we introduce the notion of $\lambda_e$-closed hyperideal in a hyperring and study some of its fundamental properties in Krasner hyperrings. |
| format | Article |
| id | doaj-art-14aefdb6b4814f11acf0cc26884d880e |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2022-11-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-14aefdb6b4814f11acf0cc26884d880e2025-01-07T10:26:23ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052022-11-01113335610.22103/jmmrc.2022.18862.11953280On hyperideals of Krasner hyperrings based on derived unitary ringsSeyed Shahin Mousavi0Morteza Jafarpour1Hojat Babaei2Irina Cristea3Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, IranMathematics Department, Vali-e-Asr University of Rafsanjan, Rafsanjan,IranDepartment of Mathematics, Islamic Azad University, Kerman Branch, Kerman, IranCenter for Information Technologies and Applied Mathematics, University of Nova Gorica, SloveniaIn this paper first, we introduce and analyze the strongly regular relations $\lambda^*_{e}$ and $\Lambda^*_{e}$ on a hyperring such that the derived quotient ring is unitary and unitary commutative, respectively. Next, we define and study the notion of $\lambda_e$-parts in a hyperring and characterize the $\lambda_e$-parts in a $\lambda_e$-strong hyperring $R$. Finally, we introduce the notion of $\lambda_e$-closed hyperideal in a hyperring and study some of its fundamental properties in Krasner hyperrings.https://jmmrc.uk.ac.ir/article_3280_e7c505906e6c975953a26e9569f6a5a5.pdf(krasner) hyperringstrongly regular relation$lambda_e$-closed hyperideal |
| spellingShingle | Seyed Shahin Mousavi Morteza Jafarpour Hojat Babaei Irina Cristea On hyperideals of Krasner hyperrings based on derived unitary rings Journal of Mahani Mathematical Research (krasner) hyperring strongly regular relation $lambda_e$-closed hyperideal |
| title | On hyperideals of Krasner hyperrings based on derived unitary rings |
| title_full | On hyperideals of Krasner hyperrings based on derived unitary rings |
| title_fullStr | On hyperideals of Krasner hyperrings based on derived unitary rings |
| title_full_unstemmed | On hyperideals of Krasner hyperrings based on derived unitary rings |
| title_short | On hyperideals of Krasner hyperrings based on derived unitary rings |
| title_sort | on hyperideals of krasner hyperrings based on derived unitary rings |
| topic | (krasner) hyperring strongly regular relation $lambda_e$-closed hyperideal |
| url | https://jmmrc.uk.ac.ir/article_3280_e7c505906e6c975953a26e9569f6a5a5.pdf |
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