Let K, I and J be ideals of ring R such that both I and J are subsets of Kwith I C J. Then show that K /l is subring of R/I and J /1 is an ideal ofK/I. Moreover, show that (K/I)/0/!) = K/J. Can we deduce that(R/J)/(K/J) = R/K ?

Given:- K,I and J be ideals of Ring R Such that I⊂J⊂K (i) Claim: K/I is subring of R/I ∀r.s∈R K⊂R…

Answered: Let K, I and J be ideals of ring R such…

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 10E: Let I1 and I2 be ideals of the ring R. Prove that the set I1I2=a1b1+a1b2+...+anbnaiI1,biI2,nZ+ is an...

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Let K, I and J be ideals of ring R such that both I and J are subsets of K with I C J. Then show that K /l is subring of R/I and J /1 is an ideal of K/I. Moreover, show that (K/I)/0/!) = K/J. Can we deduce that (R/J)/(K/J) = R/K ?