Correct the definition of the italicized term without reference to the text, if correction is needed, so

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Correct the definition of the italicized term without reference to the text, if correction is needed, so that it is in a form acceptable for publication.  

The kernel of a homomorphism ∅ mapping a ring R into a ring R' is {∅(r) = 0'|r ∈ R}.

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