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- Title
On *-n-derivations in rings with involution.
- Authors
Ashraf, Mohammad; Siddeeque, Mohammad Aslam
- Abstract
Let R be a *-ring. In this paper we introduce the notion of *-n-derivation in R. An additive mapping x → x* of R into itself is called an involution on R if it satisfies the conditions: (i) (x*)* = x, (ii) (xy)* = y*x* for all x, y ∊ R. A ring R equipped with an involution '*' is called a *-ring. It is shown that if a prime *-ring R admits a nonzero *-n-derivation (resp. a reverse *-n-derivation) D, then R is commutative. Further, some related properties of *-n-derivation in a semiprime *-ring have also been investigated. Finally, a structure theorem for *-n-derivation has been obtained.
- Subjects
RINGS with involution; FUNCTIONAL analysis; CALCULUS of variations; APPROXIMATION theory; DENSITY functionals; MATHEMATICAL analysis
- Publication
Georgian Mathematical Journal, 2015, Vol 22, Issue 1, p9
- ISSN
1072-947X
- Publication type
Article
- DOI
10.1515/gmj-2014-0063