I'm trying to prove this problem out of Allan Clark's Elements of abstract algebra.(adsbygoogle = window.adsbygoogle || []).push({});

Given an epimorphism [tex]\phi[/tex] from R -> R'

Prove that:

[tex]\phi^{-1}[/tex](a'b') = ([tex]\phi^{-1}[/tex]a')([tex]\phi^{-1}[/tex]b')

where a' and b' are ideals of R'

I had no trouble showing that ([tex]\phi^{-1}[/tex]a')([tex]\phi^{-1}[/tex]b') is a subset of [tex]\phi^{-1}[/tex](a'b'). But I'm having trouble with the forward direction. I'd appreciate any help/hints. Thanks.

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# Help with identity for ideals

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