Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41520151001On dimensions of derived algebra and central factor of a Lie algebra10931102676ENH.ArabyaniMashhad Branch, Islamic Azad University, Mashhad, Iran.F.SaeediMashhad Branch, Islamic Azad University, Mashhad, Iran.Journal Article20131105Some Lie algebra analogues of Schur's theorem and its converses <br />are presented. As a result, it is shown that for a capable Lie algebra L we <br />always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- <br />porting our results.http://bims.iranjournals.ir/article_676_3da7c8c3cba5c1fff10c3774678d395f.pdf