Left annihilators characterized by GPIS
Journal
Transactions of the American Mathematical Society
Journal Volume
347
Journal Issue
8
Pages
3159-3165
Date Issued
1995
Author(s)
Abstract
Let R be a semiprime ring with extended centroid C, U the right Utumi quotient ring of R, S a subring of U containing R and ρ1, ρ2 two right ideals of R. In the paper we show that ls(ρi) = ls(ρi) if and only if ρ1 and ρ2 satisfy the same generalized polynomial identities (GPIs) with coefficients in SC, where ls(ρi) denotes the left annihilator of pi in 5*. As a consequence of the result, if ρ is a right ideal of R such that Ir(ρ) = 0, then ρ and U satisfy the same GPIs with coefficients in the two-sided Utumi quotient ring of R. © 1995 American Mathematical Society.
Type
journal article