Submission date: 13 November 2007.

Abstract:

We investigate width and Krull--Gabriel dimension over commutative Noetherian rings which are "tame" according to the Klingler--Levy analysis in this setting, in particular over Dedekind-like rings and their homomorphic images. We show that both are undefined in most cases.

Mathematics Subject Classification: 03C60, 13CXX

Keywords and phrases: Artinian triad, Drozd ring, Klein ring, Dedekind-like ring, Krull--Gabriel dimension, Width, Superdecomposable pure injective module

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