This article is cited in 5 papers

Indentification of the Hilbert function and Poincaré series, and the dimension of modules over filtered rings

V. V. Bavula


Abstract: In this paper it is shown how to reconstruct a Poincaré series from a known Hilbert (integral) function of a graded module over a commutative Noetherian graded ring, and vice versa. The dimension and multiplicity of modules over a filtered ring whose associated graded ring is commutative and Noetherian are introduced. For one class of generalized Weyl algebras that includes the Weyl algebras $A_n$, the Krull dimension is computed, and Bernstein's inequality is proved and strengthened.

UDC: 512.54

MSC: Primary 16S32; Secondary 16P20, 16P40, 16P60, 16P90, 16W50

Received: 26.03.1992

 English version: Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:2, 225–246

Bibliographic databases:

• 
• 
• 
•