Increasing sequences of Betti numbers

Eugene Harrison Gover and Mark Bernard Ramras

Vol. 87 (1980), No. 1, 65–68

DOI: 10.2140/pjm.1980.87.65

Abstract

We study the sequence of Betti numbers {β_i(M)}_i≧1 of an arbitrary finitely generated nonfree module M over a commutative noetherian local ring R and show that for a certain class of rings this sequence is always nondecreasing, while for a certain subclass of rings, the subsequence {β_i(M)}_i≧2 is strictly increasing.

Mathematical Subject Classification 2000

Primary: 13H99

Secondary: 13D05

Milestones

Received: 18 October 1978

Revised: 28 February 1979

Published: 1 March 1980