On the c-Covers and a Special Ideal of Lie Algebras

Abstract

In this paper, our aim is to deal with some properties of c-covers of Lie algebras whose c-nilpotent multipliers are Hopfian. Moreover, it is proved that all c-covers of any nilpotent Lie algebra have Hopfian property and give a sufficient condition for two c-covers of such Lie algebras to be isomorphic. Also, we introduce a special ideal, denoted by $$ Z_{c}^{*} (L) $$ in every Lie algebra $$ L $$ , which is the intersection of special subalgebras, then give another form of this ideal and study the connection between this ideal and the concept of the c-nilpotent multiplier. Finally, we prove that if $$ L $$ is a Lie algebra for which $$ M^{(c)} \left( L \right) $$ is Hopfian, then the c-center of every c-stem cover of $$ L $$ is mapped onto $$ Z_{c}^{*} (L) $$ .