Back to Search
Start Over
Commutators with idempotent values on multilinear polynomials in prime rings.
- Source :
- Proceedings of the Indian Academy of Sciences: Mathematical Sciences; Feb2017, Vol. 127 Issue 1, p91-98, 8p
- Publication Year :
- 2017
-
Abstract
- Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R, f (x<subscript>1</subscript>, . . . , x<subscript>n</subscript>) a multilinear polynomial over C, ρ a nonzero right ideal of R andm > 1 a fixed integer such that ([d(f(r<subscript>1</subscript>, . . . , r<subscript>n</subscript>)), f(r<subscript>1</subscript>, . . . , r<subscript>n</subscript>)])<superscript>m</superscript> = [d(f(r<subscript>1</subscript>, . . . , r<subscript>n</subscript>)), f(r<subscript>1</subscript>, . . . , r<subscript>n</subscript>)] for all r<subscript>1</subscript>, . . . , r<subscript>n</subscript> ∈ ρ. Then either [f(x<subscript>1</subscript>,..., x<subscript>n</subscript>), x<subscript>n+1</subscript>]x<subscript>n+2</subscript> is an identity for ρ or d(ρ)ρ = 0. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02534142
- Volume :
- 127
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Proceedings of the Indian Academy of Sciences: Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 121051278
- Full Text :
- https://doi.org/10.1007/s12044-016-0316-1