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ON COMMUTATIVITY OF PRIME RINGS WITH LEFT GENERALIZED DERIVATIONS.
- Source :
- Palestine Journal of Mathematics; 2020, Vol. 9 Issue 1, p126-131, 6p
- Publication Year :
- 2020
-
Abstract
- Let R be a prime ring with center Z(R), central closure RC, right Martindale quotient ring Q<subscript>r</subscript>, F a left generalized derivation and I a nonzero right ideal of R which is semiprime as a ring. We proved in this article that if one of the following conditions holds: (i) F(x o y) ± x o y = 0 (ii) F(xy) ± xy ∈ Z(R) (iii) F(x)F(y) ± xy ∈ Z(R) (iv) F([x,y]) = ±[F(x), y] (v) F(x o y) = ±(F(x) o y) for all x, y ∈ I, then R is commutative or there exists q ∈Q<subscript>r</subscript>(RC) such that F(x) = qx for all x ∈ R. [ABSTRACT FROM AUTHOR]
- Subjects :
- QUOTIENT rings
Subjects
Details
- Language :
- English
- ISSN :
- 22195688
- Volume :
- 9
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Palestine Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 139607841