Differential identities of lie ideals or large right ideals in prime rings
Journal
Communications in Algebra
Journal Volume
27
Journal Issue
2
Pages
793-810
Date Issued
1999
Author(s)
Abstract
Let R be a prime ring with extended centroid C U its right Utumi quotient ring and U s its two–sided Utumi quotient ring. We prove the Lie ideal case of Kharchenko’s theorem: If is a reduced differential identity for a noncommutative Lie ideal of R, then ø(Z ij) is a GPI for [R, R], As a consequence, we conclude that R and each noncommutative Lie ideal of R satisfy the same differential identities with coefficients in U provided that R is not a PI–ring. For the one–sided version of Kharchenko’s theorem we obtain that JR and each large right ideal of R satisfy the same differential identities with coefficients in Us .
Type
journal article