please, just answer the last 3. Thank you Let I and J be ideals of a ring R:(i) Show that I+J is the smallest ideal containing both I and J.(ii) Show that IJ is an ideal contained in I N J.(iii)Show by example that IJ #InJ.(iv) Show that if R is commutative and I+J = R, then IJ = INJ.

Answered: Let I and J be ideals of a ring R: (i)…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 8E: Exercises If and are two ideals of the ring , prove that the set is an ideal of that contains...

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Let I and J be ideals of a ring R: (i) Show that I+J is the smallest ideal containing both I and J. (ii) Show that IJ is an ideal contained in I N J. (iii) Show by example that IJ #InJ. (iv) Show that if R is commutative and I+J = R, then IJ = INJ.