Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40420140801Quintasymptotic sequences over an ideal and quintasymptotic cograde941959543ENS.JahandoustDepartment of Mathematics‎, ‎University of TabrizR.NaghipourDepartment of Mathematics‎, ‎University of Tabriz‎Journal Article20130108Let $I$ 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 to show that they play a role analogous to quintessential sequences
over $I$ and quintessential cograde of $I$. 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. Also, we use this cograde to characterize two classes
of local rings.http://bims.iranjournals.ir/article_543_ddf8b69842a1acade52b2e460b55187e.pdf