Details:
Title  Gröbner–Shirshov bases for Lie algebras over a commutative algebra  Author(s)  Leonid A. Bokut, YuFu Chen  Type  Article in Journal  Abstract  In this paper we establish a Gröbner–Shirshov bases theory for Lie algebras over commutative rings. As applications we give some new examples of special Lie algebras (those embeddable in associative algebras over the same ring) and nonspecial Lie algebras (following a suggestion of P.M. Cohn (1963) [28]). In particular, Cohnʼs Lie algebras over the characteristic p are nonspecial when p = 2 , 3 , 5 . We present an algorithm that one can check for any p, whether Cohnʼs Lie algebras are nonspecial. Also we prove that any finitely or countably generated Lie algebra is embeddable in a twogenerated Lie algebra.  Keywords  Lie algebra over a commutative ring, Lyndon–Shirshov word, Gröbner–Shirshov basis  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869311002341 
Language  English  Journal  Journal of Algebra  Volume  337  Number  1  Pages  82  102  Year  2011  Edition  0  Translation 
No  Refereed 
No 
