Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401On co-Noetherian dimension of rings113122394ENA.HaghanyIsfahan University of TechnologyM. R.VedadiIsfahan University of TechnologyJournal Article20100305We define and study<br />co-Noetherian dimension of rings for which the injective envelope<br />of simple modules have finite Krull-dimension. This is a Morita<br />invariant dimension that measures how far the ring is from being<br />co-Noetherian. The co-Noetherian dimension of certain rings,<br />including commutative rings, are determined. It is<br /> shown that the class ${\mathcal W}_n$ of rings with co-Noetherian dimension $\leq<br />n$ is closed under homomorphic images and finite normalizing<br />extensions, and that for each $n$ there exist rings with<br />co-Noetherian dimension $n$. The possible relations between Krull<br /> and co-Noetherian dimensions are investigated, and examples are provided to<br /> show that these<br /> dimensions are independent of each<br />other.http://bims.iranjournals.ir/article_394_22246e6a6d66013fdfd1ed4b2e6cbbf3.pdf