On the ideals of a lie ring of derivations

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Abstract

Let R be a commutative ring, and D a Lie subring and an R-submodule of Der(R) such that R is D-semiprime (or D-prime). We investigate the structure of the ideals of D as Lie rings. As a consequence, we give a necessary and sufficient condition for the ideals of D to be semiprime (or prime, respectively) Lie rings.

Original languageEnglish
Pages (from-to)2396-2404
Number of pages9
JournalCommunications in Algebra
Volume37
Issue number7
DOIs
Publication statusPublished - 2009 Jul 1

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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