On the Jacobson radical of constants of derivations

JOURNAL OF ALGEBRA

卷:401

Article

Grzeszczuk, Piotr

关键词: Derivations of rings;    Constants of derivations;    Jacobson radical;    Artinian ring;    Semilocal ring;   

DOI  :  10.1016/j.jalgebra.2013.11.024

来源: Elsevier

【 摘 要 】

Let R be a semiprimitive algebra, d its algebraic derivation and R-d = ker d the subalgebra of constants of d. It is proved that the Jacobson radical J(R-d) of R-d is nilpotent. It is also shown that the following properties are equivalent: R-d is semilocal; R is semisimple Artinian; R-d is left and right Artinian. (C) 2013 Elsevier Inc. All rights reserved.

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