Let I be an ideals of a ring R and S C R: (i) Show that InS is an ideal of S. Is it also an ideal of R? (ii) Either prove or give counterexample that every ideal of S is of the type InS for some ideal I of R. (iii) Show that if I n S homomorphism. {OR} then 7(S) = S, where T : R → R/I is the projection %3D

Let I be an ideals of a ring R and S C R: (i) Show that InS is an ideal of S. Is it also an ideal of R? (ii) Either prove or give counterexample that every ideal of S is of the type InS for some ideal I of R. (iii) Show that if I n S homomorphism. {OR} then 7(S) = S, where T : R → R/I is the projection %3D

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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