Graded Artin algebras, rational series, and bounds for homological dimensions (Q1086656)

The author associates to every finitely generated graded module over a graded finite dimensional algebra a rational power series which is slightly different from the usual Poincaré-Betti series. Using rationality he is able to prove that the finitistic dimension conjecture is valid for a certain class of finitely generated graded modules (called special modules). As a consequence he obtains a proof of the Nakayama conjecture for graded artin algebras which is different from the one given by \textit{G. V. Wilson} [J. Algebra 85, 390-398 (1983; Zbl 0519.18012)]. He also uses rationality to give bounds for the global dimension of a graded artin algebra in terms of graded length and the number of nonisomorphic simple modules.