"A Graded Algebra with a Non-Rational Hilbert Series", Journal of Algebra, 62(1980), p. 228-231.

Abstract: Let R be an associative (but not necessarily commutative) graded algebra over a field K. Thus R = R0 + R1 + ... where R0 = K and RiRj contained in Ri+j. If each homegeneous component Rn is a finite-dimensional vector space over K then the Hilbert series of R is the formal power series F(R,lamda)= sum over n from 0 to infinity of (dim:n(Rn))*lamda**n. V. E. Govorov has conjectured that if R is finitely-generated and finitely-presented then F(R,lamda) is a rational function. Here we give a counterexample to this conjecture.

[ IBM Research home page | James B. Shearer's home page | Up ]
[ IBM home page | Order | Search | Contact IBM | Help | (C) | (TM) ]