naa a22 4500 510782809 CHVBK 20180411083253.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0110-4 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0110-4 Algebraic properties of codimension series of PI -algebras [Elektronische Daten] [Silvia Boumova, Vesselin Drensky] Let c n (R), n = 0, 1, 2, ..., be the codimension sequence of the PI-algebra R over a field of characteristic 0 with T-ideal T(R) and let c(R, t) = c 0(R) + c 1(R)t + c 2(R)t 2 + ... be the codimension series of R (i.e., the generating function of the codimension sequence of R). Let R 1,R 2 and R be PI-algebras such that T(R) = T(R1)T(R 2). We show that if c(R 1, t) and c(R 2, t) are rational functions, then c(R, t) is also rational. If c(R 1, t) is rational and c(R 2, t) is algebraic, then c(R, t) is also algebraic. The proof is based on the fact that the product of two exponential generating functions behaves as the exponential generating function of the sequence of the degrees of the outer tensor products of two sequences of representations of the symmetric groups S n . Hebrew University Magnes Press, 2013 Boumova Silvia Higher School of Civil Engineering "Lyuben Karavelov”, 175 Suhodolska Str., 1373, Sofia, Bulgaria aut Drensky Vesselin Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 593-611 0021-2172 195:2<593 2013 195 11856 https://doi.org/10.1007/s11856-012-0110-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0110-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Boumova Silvia Higher School of Civil Engineering "Lyuben Karavelov”, 175 Suhodolska Str., 1373, Sofia, Bulgaria aut NATIONALLICENCE 700 1- Drensky Vesselin Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 593-611 0021-2172 195:2<593 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer