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Quintasymptotic sequences over an ideal and quintasymptotic cograde

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 \cite{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.

preprint2013arXivOpen access
Saeed JahandoustReza Naghipour
math.AC
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Saeed JahandoustReza Naghipour

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