Abstract: Let R be a commutative ring with non-zero identity and M be a unital Rmodule. Then M is called Dedekind finite if whenever N is a submodule of M such that M is isomorphic to the module M ⊕ N, then N = 0. The ring R is called FD F-ring if any Dedekind finite R-module is finitely generated. In this note, we show that a commutative ring R is an FD F-ring if and only if it is an Artinian principal ideal ring.
Publication Year: 2011
Publication Date: 2011-01-01
Language: en
Type: article
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