Bahturin, Y.; Giambruno, A.; Zaicev, M. Codimension growth and graded identities. (English) Zbl 0968.16007 Bahturin, Yu. (ed.), Algebra. Proceedings of the international algebraic conference on the occasion of the 90th birthday of A. G. Kurosh, Moscow, Russia, May 25-30, 1998. Berlin: Walter de Gruyter. 57-76 (2000). This is a well written survey on recent and important results concerning the numerical characteristics of various ideals of identities. First the authors give an account of the growth of the codimensions of an associative PI algebra (over a field of characteristic 0), then they expose the known results in the case of identities in Lie algebras. They treat the graded versions of the above types of identities and the involution ones as well. Applications to other kinds of algebras with polynomial identities such as Jordan and alternative algebras are given as well. The bibliography is quite extensive and this will help the reader interested in the topic.For the entire collection see [Zbl 0933.00023]. Reviewer: Plamen Koshlukov (Campinas) Cited in 3 Documents MSC: 16R10 \(T\)-ideals, identities, varieties of associative rings and algebras 16R30 Trace rings and invariant theory (associative rings and algebras) 17B01 Identities, free Lie (super)algebras Keywords:codimension sequences; graded identities; growth; identities with involution; ideals of identities; PI algebras PDFBibTeX XMLCite \textit{Y. Bahturin} et al., in: Algebra. Proceedings of the international algebraic conference on the occasion of the 90th birthday of A. G. Kurosh, Moscow, Russia, May 25--30, 1998. Berlin: Walter de Gruyter. 57--76 (2000; Zbl 0968.16007)