2013•International Journal of AlgebraOpen access
On commutative DQA-rings
Mamadou Baïlo Barry, Papa Cheikhou Diop, Abdou Diouf
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Abstract
Let R be a commutative ring and M be a unital R-module. Then M is said to be quasi-Artinian if it contains an essential Artinian submodule. 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 DQA-ring if any Dedekind finite R-module is quasi-Artinian. In this note we show that a commutative ring R is a DQA-ring if and only if it is an Artinian principal ideal ring.