Let f: R → S be a ring homomorphism and T ≤ S. Prove that K = { r ∈ R : f (r) = 0s} and P = { r ∈ R : f (r) ∈ T } are both subrings of R. Explain why the result for K is a special case of the result for P

Let f: R → S be a ring homomorphism and T ≤ S. Prove that K = { r ∈ R : f (r) = 0s} and P = { r ∈ R : f (r) ∈ T } are both subrings of R. Explain why the result for K is a special case of the result for P

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let f: R → S be a ring homomorphism and T ≤ S. Prove that K = { r ∈ R : f (r) = 0_s} and
P = { r ∈ R : f (r) ∈ T } are both subrings of R. Explain why the result for K is a special case of
the result for P

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