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arXiv · 2502.17965

On derivations and semiprime ideal of rings

Gurninder Singh Sandhu·Nadeem Ur Rehman
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Abstract

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.

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Gurninder Singh Sandhu, Nadeem Ur Rehman. 2025-02-25. On derivations and semiprime ideal of rings. https://arxiv.org/abs/2502.17965

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