Rings and ideals

See attached 1-5...

Let R be a ring with identity c and let A be an ideal....

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This provides examples of completing proofs regarding rings and ideals.

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Ring Theory : Prove that if an ideal U of a ring R contains a unit of R then U = R . - Prove that if an ideal U of a ring R contains a unit of R then U = R .
Prove properties of a ring with additive identity 0. - Let R be a ring with additive identity 0. Prove the following: (a) For all a in R, a(0) = 0. (b) a(-b)=-(ab). NOTE: see attached word document for clearer notations.
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Ring Homomorphisms and Ideals - Let : R->Q be a ring homomorphism , and suppose that I is a non-trivial ideal of R. Prove or disprove that (I)={ (i)| i I } is necessary an ideal of Q. Let : R->Q be a ONTO ring homomorphism ...