QUESTION 10 Let f:R S be a ring homomorphism. (i) Prove that if K is a subring of R then F(K) is a subring of S (ii) Prousthat f is one to one if and only if Kerf={0}· Attach File Browse Local Files

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Q: (a) Let R be a ring and S a subset of R. What does it mean to say that S is a subring of R?

A: a. S is a subset of R. A non-empty subset S of R is a subring if a, b ∈ S ⇒ a - b, ab ∈ S. A subring…

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A: We can solve this using defination of ideals ,prime ideals ,quotient ideals

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Q: = (19) Let om : Z → Zm be the ring homomorphism defined by σm(a) = remainder of division of a by m.…

A: Ans-19)We are given in the question (19) Let om Z→ Zm be the ring homomorphism defined by om (a) = =…

Q: 2. Let s-{(소)아 2a S = 26 2a Assume that S is a subring of M2(Q). Prove that S is isomorphic to Q[V2]…

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Q: et FCK be a field extension and let R be the alg K. Then R is a subfield of K and FCR.

A: let alpha and beta are in R

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Q: a) Let p: Z → Z be defined by ø(n) = n/2 if n is even 3n + 1 if n is odd Check %3| whether p is well…

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Q: Let f:R, → R, and let g : R, → R, be two ring isomorphisms. If ø = g• f , then 2- (e2) =

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Q: Exercise: Prove that the homomorphism f:R R of the ring R onto the ring R' is isomorphism if and…

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Q: (9) Let R be a ring such that x² = x for any x ЄR. (a) Prove that it is commutative. (b) Can R be an…

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Q: 6 Define f:Z- 42 by f(x) - 4x, for all x €Z. Then: (a) f is a ring epimorphism. (b) / is a ring…

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