On generalized derivations involving prime ideals with involution

Nadeem ur Rehman; Hafedh M.  Alnoghashi; Motoshi  Hongan

doi:10.3842/umzh.v75i8.7064

Nadeem ur Rehman Department of Mathematics, Aligarh Muslim University, India https://orcid.org/0000-0003-3955-7941
Hafedh M. Alnoghashi Department of Computer Science, College of Engineering and Information Technology, Amran University, Yemen
Motoshi Hongan Maniwa, Okayama, Japan

DOI: https://doi.org/10.3842/umzh.v75i8.7064

Keywords: Prime ideal, involution, generalized derivations, commutativity

Abstract

UDC 512.5

We study the structure of the quotient ${A}/{P}$, where ${A}$ is any ring with involution $*$ and ${P}$ is a prime ideal of ${A}$. With an aim to construct a ring with involution of this kind, we study the behavior of generalized derivations satisfying the algebraic identities involving prime ideals. As a consequence, currently existing results in this field are enhanced.

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