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Let $f:R\rightarrow S$ be an isomorphism. Prove that if we let $R$ be a principal ideal ring it follows that $S$ is a principal ideal ring too.

How should I begin the proof?

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    What is isomorphic?2011-05-11
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    If the map is an isomorphism, then everything is obvious (the ideals are the same, the generators are the same, everything you want is preserved by isomorphisms). What you probably want is for the map to be surjective.2011-05-11
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    @Zev Chonoles: I do not think that it is certain that the OP wanted to talk about isomorphisms.2011-05-11
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    @user9325: The original text was "Let R --> S be an isomorphic". It would make sense to have "Let $R$ and $S$ **be** isomorphic", but the existence of both the word "an" *and* the arrow notation, indicates to me that the isomorphism was intended to be an explicit part of this question.2011-05-11
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    Also I have no compunctions about changing the title to something that is descriptive of what the question is about.2011-05-11
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    @David: Does your definition of "isomorphism" require invertibility of the function, or only for the functions to be one-to-one? (See the comments in this recent question: http://math.stackexchange.com/questions/36784/abstract-algebra-ring-homomorphism2011-05-12

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