Actions of generalized derivations on prime ideals in $*$-rings with applications

Year 2023, Volume: 52 Issue: 5, 1219 - 1228, 31.10.2023

Adnan Abbasi , Abdul Khan , Mohammad Salahuddin Khan

https://doi.org/10.15672/hujms.1119353

Abstract

In this paper, we make use of generalized derivations to scrutinize the deportment of prime ideal satisfying certain algebraic $*$-identities in rings with involution. In specific cases, the structure of the quotient ring $\mathscr{R}/\mathscr{P}$ will be resolved, where $\mathscr{R}$ is an arbitrary ring and $\mathscr{P}$ is a prime ideal of $\mathscr{R}$ and we also find the behaviour of derivations associated with generalized derivations satisfying algebraic $*$-identities involving prime ideals. Finally, we conclude our paper with applications of the previous section's results.

Keywords

Derivation, generalized derivation, involution, prime ideal

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