The kernel and range inclusions of integral derivations in semiprime rings
Resource
Journal of algebra 320 (7): 2643-2658
Journal
Journal of Algebra
Journal Volume
320
Journal Issue
7
Pages
2643-2658
Date Issued
2008
Author(s)
Abstract
Let R be a semiprime ring with extended centroid C and with symmetric Martindale quotient ring Q. For a derivation δ of R and an ideal I of R, define KerI (δ) over(=, def .) {r ∈ I | δ (r) = 0} and RI (δ) over(=, def .) δ (I). Let δ, δ′ be derivations of R such that δ is C-integral and has the associated X-inner derivation ad (a), where a ∈ Q. The main results of this paper (Theorem 3.5) are the following two equivalences: (1)KerI (δ) ⊆ KerR (δ′) for an essential ideal I of R if and only if δ′ = ∑i ≥ 1 μi δi + ad (b) for some μi ∈ C and some b ∈ C [a].(2)RI (δ′) ⊆ RR (δ) for an essential ideal I of R if and only if δ′ = ∑i ≥ 1 μi δi + ad (b) for some μi ∈ C with ∑i ≥ 1 (- 1)i δi (μi) = 0 and some b ∈ C [a]. © 2008 Elsevier Inc. All rights reserved.
Type
journal article
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