Maps preserving triple product on rings

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O.Box 47416-1468, Babolsar, Iran.

10.22103/jmmrc.2021.16645.1124

Abstract

Let R and R0 be two unital rings such that R contains a non-
trivial idempotent P1. If R is a prime ring, we characterize the form of bijective
map ' : R ! R0 which satis es '(ABP) = '(A)'(B)'(P), for every A;B 2 R
and P 2 fP1; P2g, where P2 := I 􀀀 P1 and I is the unit member of R. It is
shown that ' is an isomorphism multiplied by a central element. Finally, we
characterize the form of ' : R ! R which satis es '(P)'(A)'(P) = PAP,
for every A 2 R and P 2 fP1; P2g.

Keywords


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Volume 10, Issue 2
Special Issue Dedicated to Professor M. Radjabalipour on the occasion of his 75th birthday.
Summer and Autumn 2021
Pages 1-8
  • Receive Date: 23 October 2020
  • Revise Date: 26 December 2020
  • Accept Date: 15 April 2021