An Upper Bound on the Reduction Number of an Ideal

Abstract

Abstract. Let A be a commutative ring and I an ideal of A with a reduction Q. In this paper we give an upper bound on the reduction number of I with respect to Q, when a suitable family of ideals in A is given. As a corollary it follows that if some ideal J containing I satisfies J 2 = QJ, then I v+2 = QI v+1 , where v denotes the number of generators of J/I as an A-module.