Cheng-Kai Liu
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.
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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.
Key concepts: Semiprime ring, Subring, Mathematics, Pure mathematics, Semiprime, Prime ring, Prime (order theory), Noncommutative ring