On derivations and semiprime ideal of rings
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917104368746496 |
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| author | Sandhu, Gurninder Singh Rehman, Nadeem Ur |
| author_facet | Sandhu, Gurninder Singh Rehman, Nadeem Ur |
| contents | Let $R$ be an associative ring with a nonzero ideal $I$ and a semiprime ideal $T$ such that $T\subsetneq I.$ Let $K$ be a nonempty subset of $R$ and $d:R\to R$ be a derivation of $R$, if $[d(x),x]\in T$ for all $x\in K,$ then $d$ is said to be a $T$-commuting derivation on $K.$ We show that if some specific $T$-valued differential identities are imposed on $I$, then d is $T$-commuting. Moreover, we provide semiprime ideal variant of some known results on derivations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On derivations and semiprime ideal of rings Sandhu, Gurninder Singh Rehman, Nadeem Ur Commutative Algebra Rings and Algebras 16W25, 16N60 Let $R$ be an associative ring with a nonzero ideal $I$ and a semiprime ideal $T$ such that $T\subsetneq I.$ Let $K$ be a nonempty subset of $R$ and $d:R\to R$ be a derivation of $R$, if $[d(x),x]\in T$ for all $x\in K,$ then $d$ is said to be a $T$-commuting derivation on $K.$ We show that if some specific $T$-valued differential identities are imposed on $I$, then d is $T$-commuting. Moreover, we provide semiprime ideal variant of some known results on derivations. |
| title | On derivations and semiprime ideal of rings |
| topic | Commutative Algebra Rings and Algebras 16W25, 16N60 |
| url | https://arxiv.org/abs/2502.17965 |