$LetDbe a principal ideal domain. IfI_{1},I_{2},...is a set of ideals such thatI_{1}⊂I_{2}⊂⋯,then there exists an integerNsuch thatI_{n}=I_{N}for alln≥N $

begin{array}{l}{text { Let } D text { be a principal ideal domain. If } I_{1}, I_{2}, ldots text { is a set of ideals such that } I_{1} subset} \ {I_{2} subset cdots, text { then there exists an integer } N text { such that } I_{n}=I_{N} text { for all } n geq N}end{array}

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