Let I,J be the ideals of a ring P. Show that the sets (a)lJ = {a,b, +.….+a,b, :a, E1,b, E J,n=1,2,...} (b)l + J={a+b:a€l,bEJ} (c)InJ are the ideals of the ring, and prove If 1+J=P, then INJ=IJ
Let I,J be the ideals of a ring P. Show that the sets (a)lJ = {a,b, +.….+a,b, :a, E1,b, E J,n=1,2,...} (b)l + J={a+b:a€l,bEJ} (c)InJ are the ideals of the ring, and prove If 1+J=P, then INJ=IJ
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 I,J be the ideals of a ring P. Show that the sets
(a)lJ = {a,b, + .. +a,b, :a, E1,b, €J,n=1,2,...}
(b)l+J- {a+b:aE1,bEJ}
(c)/NJ
are the ideals of the ring, and prove If 1+J=P, then InJ=IJ](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff79bbcda-ba0d-4938-b53a-59a6b8504288%2Fd4b65bab-c43d-4a9a-96e5-32725b34dea6%2Fvr5ukc_processed.png&w=3840&q=75)
Transcribed Image Text:Let I,J be the ideals of a ring P. Show that the sets
(a)lJ = {a,b, + .. +a,b, :a, E1,b, €J,n=1,2,...}
(b)l+J- {a+b:aE1,bEJ}
(c)/NJ
are the ideals of the ring, and prove If 1+J=P, then InJ=IJ
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