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

Authors : Adnan Abbasi, Abdul Khan, Mohammad Salahuddin Khan

Pages : 1219-1228

Doi:10.15672/hujms.1119353

View : 169 | Download : 293

Publication Date : 2023-10-31

Article Type : Research Paper

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