If is a ring with identity, and is a homomorphism from to a ring , prove that is an idempotent in . [Idempotent were defined in Exercise 3 of Section 3.2.]
Hence it is proved that is an idempotent in .
If any ring has elements such that, , then, addition and multiplication of the function of its elements is respectively given by:
We have a homomorphism of rings as:
In this case, we get:
Hence proved, is an idempotent in .
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