Affiliation:
1. Madanpalle Institute of Technology and Science
2. King Abdulaziz University
3. Aligarh Muslim University
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.
Subject
Geometry and Topology,Statistics and Probability,Algebra and Number Theory,Analysis
Reference24 articles.
1. [1] S. Ali and N.A. Dar, On $\ast$-centralizing mappings in rings with involution, Georgian
Math. J. 21 (1), 25–28, 2014.
2. [2] S. Ali, N.A. Dar and A.N. Khan, On strong commutativity preserving like maps in
rings with involution, Miskolc Math. Notes 16 (1), 17–24, 2015.
3. [3] K.I. Beidar, On functional identities and commuting additive mappings, Comm. Algebra
26, 1819–1850, 1998.
4. [4] K.I. Beidar,W.S. Martindale III and A.V. Mikhalev, Rings with generalized identities,
Monographs and Textbooks in Pure and Applied Mathematics, New York: Marcel
Dekker, Inc., 1996.
5. [5] H.E. Bell and M.N. Daif, On commutativity and strong commutativity-preserving
maps, Canad. Math. Bull. 37 (4), 443–447, 1994.
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