# On co-Noetherian dimension of rings

Document Type : Research Paper

Authors

Isfahan University of Technology

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.

Keywords

### History

• Receive Date: 05 March 2010
• Revise Date: 07 September 2010
• Accept Date: 07 September 2010