Given that (I, t.) in an ideal of the ring (R, +,), show that a) whenever (R,1,) in commutative with identity, then so is the quotient ring (R/I,+,),
Given that (I, t.) in an ideal of the ring (R, +,), show that a) whenever (R,1,) in commutative with identity, then so is the quotient ring (R/I,+,),
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 14E
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![17. Given that (I,t.) in an ideal of the ring (R, +,), whow that
a) whenever (R, 1,) in commutative with identity, then so is the quotient ring
(R/1,+,),
b) the ring (R/I,+,) may have divisors of zero, even though (R, +,) does
not have any,
c) if (R, +,) in a principal ideal ring, then so is the quotient ring (R/I,+,).
ive rims with il.untity and kt Nlonete the set of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0851a0de-a4d7-4b5f-be27-01ba24ab0a9d%2Fa4b934f6-b3d7-4fb7-984d-67d63e7b7c5a%2Feb9439_processed.jpeg&w=3840&q=75)
Transcribed Image Text:17. Given that (I,t.) in an ideal of the ring (R, +,), whow that
a) whenever (R, 1,) in commutative with identity, then so is the quotient ring
(R/1,+,),
b) the ring (R/I,+,) may have divisors of zero, even though (R, +,) does
not have any,
c) if (R, +,) in a principal ideal ring, then so is the quotient ring (R/I,+,).
ive rims with il.untity and kt Nlonete the set of
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