Certain Chain Conditions in Modules over Dedekind Domains and Related Rings
Necessary and sufficient conditions are given for a module over a Dedekind domain to satisfy the ascending chain condition on n-generated submodules for every positive integer n or on submodules with uniform dimension at most n for every positive integer n. These results are then extended to modules over commutative Noetherian domains which need not be Dedekind.
KeywordsChain conditions Dedekind domain Uniform dimension
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