Quintasymptotic sequences over an ideal and quintasymptotic cograde

Document Type : Research Paper


1 Department of Mathematics‎, ‎University of Tabriz

2 Department of Mathematics‎, ‎University of Tabriz‎


‎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 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.


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