On Jordan *-mappings in rings with involution | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 24, Issue 1, 2016, Page 15-19 PDF (407.57 K) | ||||
| DOI: 10.1016/j.joems.2014.12.006 | ||||
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| Authors | ||||
| Shakir Ali1; Nadeem Ahmad Dar2; Hassan M. Okasha3 | ||||
| 1Department of Mathematics, Faculty of Science, Rabigh, King Abdulaziz University, Jeddah-21589, Kingdom of Saudi Arabia | ||||
| 2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India | ||||
| 3Department of Statistics, Faculty of Science, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia | ||||
| 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 | ||||
| Prime ring; Involution; Jordan -derivation; Jordan left -derivation; Symmetric Jordan -biderivation; Symmetric Jordan triple -biderivation | ||||
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