Lie algebras whose inner derivations satisfy certain conditions (Q912198)

The purpose of this paper is to extend the known results on finite- dimensional Lie algebras satisfying certain conditions to not necessarily finite-dimensional Lie algebras. The conditions in question consist of: (i) Condition A [\textit{I. M. Singer}, Ann. Math., II. Ser. 56, 242-247 (1952; Zbl 0049.358)]. (ii) Conditions \(A_ k\) and \(A_{\infty}\) [\textit{A. Jôichi}, J. Sci. Hiroshima Univ., Ser. A I 31, 25-33 (1967; Zbl 0244.17004)]. (iii) Condition \(B_{\infty}\) introduced by the present authors.