1Department of of Mathematical Sciences, Isfahan University of
Technology, Isfahan 84156-83111,
2Department of Mathematical Sciences, Isfahan University of
Technology, Isfahan 84156-83111
Abstract
We define and study
co-Noetherian dimension of rings for which the injective envelope
of simple modules have finite Krull-dimension. This is a Morita
invariant dimension that measures how far the ring is from being
co-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 $leq
n$ is closed under homomorphic images and finite normalizing
extensions, and that for each $n$ there exist rings with
co-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 each
other.
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