Quintasymptotic sequences over an ideal and quintasymptotic cograde
Abstract
Let I denote an ideal of a Noetherian ring R. The purpose of this article is to introduce the concepts of quintasymptotic sequences over I and quintasymptotic cograde of I, and it is shown that they play a role analogous to quintessential sequences over I and quintessential cograde of I, given in Ra1. Also, we show that, if R is local, then the quintasymptotic cograde of I is unambiguously defined and behaves well when passing to certain related local rings. Finally, we use this cograde to characterize of two classes of local rings.
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