Invariant additive subgroups of a certain kind
type: Item
instance of: scholarly article
title: Invariant additive subgroups of a certain kind
zbMATH Open document ID: 0657.16021
DOI: 10.1007/BF02766209
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: It is shown here that if R is a prime ring with a non-zero nil right ideal and W is an additive subgroup of R which is invariant under all inner automorphisms of R induced by elements of the form \(1+x\), where x belongs to a nil right ideal of R, then either W is central or W contains a noncommutative Lie ideal J of R. By a theorem of the author and \textit{S. Montgomery} [Pac. J. Math. 42, 117-136 (1972; Zbl 0243.16018)] the Lie ideal J must, in turn, contain a Lie ideal of the form [I,R] where I is a non-zero ideal of R. The result described above extends a result, due to \textit{I. N. Herstein} [Isr. J. Math. 26, 205-208 (1977; Zbl 0343.16006)] in which subrings rather than additive subgroups were considered and which is used in the proof of the present result.
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16N60
zbMATH DE Number: 4073218
zbMATH Keywords: prime ring
zbMATH Keywords: nil right ideal
zbMATH Keywords: inner automorphisms
zbMATH Keywords: noncommutative Lie ideal
zbMATH Keywords: additive subgroups
author: Charles Lanski
reviewed by: David A. Jordan
MaRDI profile type: Publication
cites work: Invariant Submodules of Simple Rings
cites work: Lie Simplicity of a Special Class of Associative Rings
cites work: On invariant additive subgroups
cites work: Q5639810
cites work: Q4112071
cites work: Invariant subrings of a certain kind
cites work: A theorem on invariant subrings
cites work: Lie structure of prime rings of characteristic 2
cites work: Prime rings satisfying a generalized polynomial identity
description: scientific article; zbMATH DE number 4073218