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RINGS OF BOUNDED MODULE TYPE.
Abstract
The fundamental theorem of abelian groups states that finitely generated modules over a commutative principal ideal ring are direct sums of cyclic modules. This property characterizes principal ideal rings among commutative Noetherian rings. It is reasonable to ask which non-Noetherian rings satisfy the fundamental theorem. Several partial solutions have appeared during the last thirty years. The complete answer was finally obtained in 1976, [11]. For many purposes, the rings satisfying the fundamental theorem (called "FGC-rings") are too restrictive. For example, the fundamental theorem fails for Dedekind domains. Yet every finitely generated module over a Dede- kind domain is a direct sum of submodules generated by at most two elements, a property that characterizes Dedekind domains among Noetherian domains.
Subject Area
Mathematics
Recommended Citation
MIDGARDEN, BETTE GENE, "RINGS OF BOUNDED MODULE TYPE." (1978). ETD collection for University of Nebraska-Lincoln. AAI7900336.
https://digitalcommons.unl.edu/dissertations/AAI7900336