A class of principal ideal rings arising from the converse of the Chinese remainder theorem

David E. Dobbs

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-5

Abstract:

Let R be a (nonzero commutative unital) ring. If I and J are ideals of R such that R / I ⊕ R / J is a cyclic R -module,then I + J = R . The rings R such that R / I ⊕ R / J is a cyclic R -module for all distinct nonzero proper ideals I and J of R are the following three types of principal ideal rings:fields, rings isomorphic to K × L for the fields K and L , and special principal ideal rings ( R , M ) such that M 2 = 0 .

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:019607

DOI: 10.1155/IJMMS/2006/19607

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