Prime Radical and Primary decomposition of Ideals in an L subring
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915453975134208 |
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| author | Ajmal, Naseem Prajapati, Anand Swaroop |
| author_facet | Ajmal, Naseem Prajapati, Anand Swaroop |
| contents | In this paper we introduce the concept of a prime radical of an ideal of an L-ring L(mu,R) . Among various results pertaining to this concept, we prove here that prime radicals of an ideal eta, its radical , its semiprime radical S(eta) and its prime radical P(eta) , all coincide. Also we prove that for a primary ideal, its prime radical coincide with its radical. Moreover, we introduce the concept of primary decomposition and reduced primary decomposition of an ideal in an L-ring. We obtain a necessary and sufficient conditions for an ideal of an L-ring to have a primary decomposition. Some more results pertaining to the decomposition of an ideal are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14903 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prime Radical and Primary decomposition of Ideals in an L subring Ajmal, Naseem Prajapati, Anand Swaroop Rings and Algebras 13A99, 03G99 In this paper we introduce the concept of a prime radical of an ideal of an L-ring L(mu,R) . Among various results pertaining to this concept, we prove here that prime radicals of an ideal eta, its radical , its semiprime radical S(eta) and its prime radical P(eta) , all coincide. Also we prove that for a primary ideal, its prime radical coincide with its radical. Moreover, we introduce the concept of primary decomposition and reduced primary decomposition of an ideal in an L-ring. We obtain a necessary and sufficient conditions for an ideal of an L-ring to have a primary decomposition. Some more results pertaining to the decomposition of an ideal are established. |
| title | Prime Radical and Primary decomposition of Ideals in an L subring |
| topic | Rings and Algebras 13A99, 03G99 |
| url | https://arxiv.org/abs/2508.14903 |