UTA Department of Mathematics

Algebra Seminar

Date/Time/Room: Friday (10/27/2006) at 4:00 pm in 487 Pickard Hall

Speaker: William Purpura
AmeriCredit, Fort Worth, Texas


"GRADED RINGS, HILBERT POLYNOMIALS, AND DIMENSION"

Abstract: In this talk we will introduce graded rings and modules, and define Hilbert-Poincare series of additive functions on finitely generated modules. In particular, we will define Hilbert series and Hilbert polynomials, which are extremely useful devices for gathering information about a module. As a specific example, we will sketch the groundwork for the "dimension theorem" for local rings: Let (A,m) be a (Noetherian) local ring. Then the minimal number of generators of an m-primary ideal is equal to the dimension of A which is also equal to the degree of the Hilbert polynomial of A.