%0 Journal Article %T On co-Noetherian dimension of rings %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Haghany, A. %A Vedadi, M. R. %D 2012 %\ 04/01/2012 %V 38 %N 1 %P 113-122 %! On co-Noetherian dimension of rings %K Co-Noetherian %K finitely cogenerated %K Krull dimension %K normalizing extension %R %X We define and studyco-Noetherian dimension of rings for which the injective envelopeof simple modules have finite Krull-dimension. This  is a Moritainvariant dimension that measures how far the ring is from beingco-Noetherian. The co-Noetherian dimension of certain rings,including commutative rings, are determined. It is shown that the class ${\mathcal W}_n$ of rings with co-Noetherian dimension $\leqn$ is closed under homomorphic images and finite normalizingextensions, and that for each $n$ there exist rings withco-Noetherian dimension $n$. The possible relations between Krull and co-Noetherian dimensions  are investigated, and examples are provided to show that these dimensions are independent of eachother. %U http://bims.iranjournals.ir/article_394_22246e6a6d66013fdfd1ed4b2e6cbbf3.pdf