A note on generalized derivations on prime ideals

Document Type : Research Paper


1 Department of Mathematics Aligarh Muslim University Aligarh, India

2 Department of Mathematics, Seki 772, Maniwa, Okayama, Japan.


This paper investigates the structure of the quotient ring $\mathscr{R}/ \mathscr{P}$, where $\mathscr{R}$ is an arbitrary ring and $\mathscr{P}$ is a prime ideal of $\mathscr{R}$ . We show that the structure of this class of rings has a relationship with the behaviour of generalized derivations satisfying algebraic identities involving prime ideals.