Vol. 87, No. 1, 1980

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Increasing sequences of Betti numbers

Eugene Harrison Gover and Mark Bernard Ramras

Vol. 87 (1980), No. 1, 65–68
Abstract

We study the sequence of Betti numbers {βi(M)}i1 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 {βi(M)}i2 is strictly increasing.

Mathematical Subject Classification 2000
Primary: 13H99
Secondary: 13D05
Milestones
Received: 18 October 1978
Revised: 28 February 1979
Published: 1 March 1980
Authors
Eugene Harrison Gover
Mark Bernard Ramras