Abstract
A mapfof the ringRinto itself is of period 2 iff2x=xfor allx∈R; involutions are much studied examples. We present some commutativity results for semiprime and prime rings with involution, and we study the existence of derivations and generalized derivations of period 2 on prime and semiprime rings.
Highlights
Let R be a ring with center Z = Z(R), and for each x, y ∈ R, let [x, y] denote the commutator xy − yx
A map f : R → R is said to be of period 2 on S if f2(x) = x for all x ∈ S, and S is called an f-subset if f(S) = S
Assume first that ∗ is commuting on U; that is, [x, x∗] = 0 for all x ∈ U
Summary
A map f : R → R is said to be of period 2 on S if f2(x) = x for all x ∈ S, and S is called an f-subset if f(S) = S. Left) generalized derivation on R if F(xy) = F(x)y + xd(y) (resp., F(xy) = d(x)y + xF(y)) for all x, y ∈ R, where d is a derivation on R, called the associated derivation. (Note that this definition is different from that of Hvala in [2]; his generalized derivations are our right generalized derivations.). Our purpose is to study existence and properties of involutions, derivations, and generalized derivations of period 2 on certain subsets of semiprime and prime rings
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematics and Mathematical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
