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http://dx.doi.org/10.14317/jami.2022.709

SEMIPRIME RINGS WITH INVOLUTION AND CENTRALIZERS  

ANSARI, ABU ZAID (Department of Mathematics, Faculty of Science, Islamic University of Madinah)
SHUJAT, FAIZA (Department of Mathematics, Faculty of Science, Taibah University)
Publication Information
Journal of applied mathematics & informatics / v.40, no.3_4, 2022 , pp. 709-717 More about this Journal
Abstract
The objective of this research is to prove that an additive mapping T : R → R is a left as well as right centralizer on R if it satisfies any one of the following identities: (i) T(xnyn + ynxn) = T(xn)yn + ynT(xn) (ii) 2T(xnyn) = T(xn)yn + ynT(xn) for each x, y ∈ R, where n ≥ 1 is a fixed integer and R is any n!-torsion free semiprime ring. In addition, we talk over above identities in the setting of *-ring(ring with involution).
Keywords
Semiprime ring; left(right) centralizer; involution;
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