Let T be ring containing elements e, f, both # 0T, such that e + f = 1r , e² = e, f² = f , and e · f = 0r . Show that then the ideals R := T · e and S := subrings of T, and that the ring T is isomorphic to the ring R x S defined in 1) above. T f are rings but not

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Q: If A, B, C are ideals of a ring R such that BCA, prove that An (B + C) = B+(AnC) = (A B) + (AnC).

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Q: If the rings R and S are isomorphic, show that R[x] and S[x] areisomorphic.

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Q: 8. If 1 and 2 are two ideals of the ring R, prove that the set 1₁+= {x+yx Eh, yЄh} is an ideal of R…

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Q: 1. Prove that if S is a subring of a ring R then the following are true: (a) Os = OR (b) if 1R € S,…

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