Problem 17.33: Let I, J be ideals in a ring R and define their sum I + J as I + J = {x+y: € I, ye J}. a) Show that I + J is an ideal.. b) Find 6Z+14Z in (Z, +,-).
Problem 17.33: Let I, J be ideals in a ring R and define their sum I + J as I + J = {x+y: € I, ye J}. a) Show that I + J is an ideal.. b) Find 6Z+14Z in (Z, +,-).
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 6E: Exercises
Find two ideals and of the ring such that
is not an ideal of .
is an ideal of .
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![Problem 17.33: Let I, J be ideals in a ring R and define their sum I + J as
I + J = {x+y: € I, ye J}.
a) Show that I + J is an ideal..
b) Find 6Z+14Z in (Z, +,-).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0c3f06e-3e86-4116-90aa-57831e29172c%2Fbad11f9e-b83f-49bf-8e29-425dfa8d9031%2Fevml9s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 17.33: Let I, J be ideals in a ring R and define their sum I + J as
I + J = {x+y: € I, ye J}.
a) Show that I + J is an ideal..
b) Find 6Z+14Z in (Z, +,-).
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