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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/2401.08535 |
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| _version_ | 1866911758973665280 |
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| author | Nongsiej, Raplang Buhphang, Ardeline Mary |
| author_facet | Nongsiej, Raplang Buhphang, Ardeline Mary |
| contents | The class of nil-essential ideals is a generalisation of the class of essential ideals. Every nil-essential ideal of a reduced ring is essential. Therefore the intersection of all nil-essential ideals over a reduced ring $R$ is the socle of $R$. In this note, we apply this generalisation to give a new criteria of semisimplicity in terms of nil-essentiality of ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08535 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nil-Essential Ideals Nongsiej, Raplang Buhphang, Ardeline Mary Rings and Algebras 16D10, 16D40, 16D60 The class of nil-essential ideals is a generalisation of the class of essential ideals. Every nil-essential ideal of a reduced ring is essential. Therefore the intersection of all nil-essential ideals over a reduced ring $R$ is the socle of $R$. In this note, we apply this generalisation to give a new criteria of semisimplicity in terms of nil-essentiality of ideals. |
| title | Nil-Essential Ideals |
| topic | Rings and Algebras 16D10, 16D40, 16D60 |
| url | https://arxiv.org/abs/2401.08535 |