Mathematika

Research Article

On the relation type of large powers of an ideal

Bernard Johnstona1 and Daniel Katza2

a1 Department of Mathematics, Florida Atlantic University, Boca Raton, FL 33431. U.S.A.

a2 Department of Mathematics, University of Kansas, Lawrence, KS 60045. U.S.A.

Abstract

We prove that the relation type of all high powers of an ideal in a Noetherian ring is either one or two. It is one exactly when some power of the ideal is locally principal.

(Received January 25 1993)

Key Words:

  • 16P40: ASSOCIATIVE RINGS AND ALGEBRAS; Chain conditions, growth conditions, and other forms offiniteness; Noetherian rings and modules.