Prime Lie rings of derivations of commutative rings in characteristic 2

Chia Hsin Liu; Donald S. Passman

doi:10.1016/j.jalgebra.2006.08.035

Prime Lie rings of derivations of commutative rings in characteristic 2

Chia Hsin Liu^*, Donald S. Passman

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Let R be a commutative associative ring with 1 and let Der (R) be the Lie ring of all derivations of R. Suppose that D is a Lie subring and an R-submodule of Der (R). When R is D-prime, we give necessary and sufficient conditions for D to be Lie prime. Since results of this nature are already known for rings R of characteristic different from 2, what is really new here is the characteristic 2 case.

Original language	English
Pages (from-to)	352-364
Number of pages	13
Journal	Journal of Algebra
Volume	311
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2006.08.035
Publication status	Published - 2007 May 1

Keywords

Derivations
Lie rings
Prime Lie rings

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2006.08.035

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T1 - Prime Lie rings of derivations of commutative rings in characteristic 2

AU - Liu, Chia Hsin

AU - Passman, Donald S.

PY - 2007/5/1

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N2 - Let R be a commutative associative ring with 1 and let Der (R) be the Lie ring of all derivations of R. Suppose that D is a Lie subring and an R-submodule of Der (R). When R is D-prime, we give necessary and sufficient conditions for D to be Lie prime. Since results of this nature are already known for rings R of characteristic different from 2, what is really new here is the characteristic 2 case.

AB - Let R be a commutative associative ring with 1 and let Der (R) be the Lie ring of all derivations of R. Suppose that D is a Lie subring and an R-submodule of Der (R). When R is D-prime, we give necessary and sufficient conditions for D to be Lie prime. Since results of this nature are already known for rings R of characteristic different from 2, what is really new here is the characteristic 2 case.

KW - Derivations

KW - Lie rings

KW - Prime Lie rings

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SP - 352

EP - 364

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Prime Lie rings of derivations of commutative rings in characteristic 2

Abstract

Keywords

ASJC Scopus subject areas

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