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NOTES ON SYMMETRIC SKEW n-DERIVATION IN RINGS
- Publication Year :
- 2018
- Publisher :
- KOREAN MATHEMATICAL SOC, 2018.
-
Abstract
- WOS: 000449061700007<br />Let R be a prime ring (or semiprime ring) with center Z(R), I a nonzero ideal of R, T an automorphism of R, S : R-n -> R be a symmetric skew n-derivation associated with the automorphism T and Delta is the trace of S. In this paper, we shall prove that S(x(1),..., x(n)) = 0 for all x(1),..., x(n) is an element of R if any one of the following holds: i) Delta(x) = 0, ii) [Delta(x), T(x)] = 0 for all x is an element of I. Moreover, we prove that if [Delta(x), T(x)] is an element of Z(R) for all x is an element of I, then R is a commutative ring.
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.od......3104..55012139c315f9a9f8a5b6815d58a59d