On Jordan *-mappings in rings with involution

Authors

1 Department of Mathematics, Faculty of Science, Rabigh, King Abdulaziz University, Jeddah-21589, Kingdom of Saudi Arabia

2 Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

3 Department of Statistics, Faculty of Science, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

10.21608/joems.2016.386748

Abstract

The objective of this paper is to study Jordan -mappings in rings with involution . In
particular, we prove that if R is a prime ring with involution , of characteristic different from 2 and
D is a nonzero Jordan -derivation of R such that ½DðxÞ; x ¼ 0, for all x 2 R and
SðRÞ \ ZðRÞ – ð0Þ, then R is commutative. Further, we also prove a similar result in the setting
of Jordan left -derivation. Finally, we prove that any symmetric Jordan triple -biderivation on
a 2-torsion free semiprime ring with involution  is a symmetric Jordan -biderivation

Keywords

Journal of the Egyptian Mathematical Society
Volume 24, Issue 1
2016
Pages 15-19

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