%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