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Algebra Seminar
Date/Time/Room: Friday (10/27/2006) at 4:00 pm in 487 Pickard Hall
Speaker: William Purpura
"GRADED RINGS, HILBERT POLYNOMIALS, AND DIMENSION"Abstract: In this talk we will introduce graded rings and modules, and define HilbertPoincare 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 mprimary ideal is equal to the dimension of A which is also equal to the degree of the Hilbert polynomial of A.

