Let R be a ring with unity and ICR× R. Prove that I is an ideal of the ring R× R if and only if I = 11 x I2 for some ideals I and I2 of R.
Let R be a ring with unity and ICR× R. Prove that I is an ideal of the ring R× R if and only if I = 11 x I2 for some ideals I and I2 of R.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![b. Let R be a ring with unity and ICRX R. Prove that I is an ideal of the ring R × R if and
only if I = 11 × I2 for some ideals I1 and I2 of R.
Prove that neither 2 nor 17 are prime elements in Z[i] (the ring of Gaussian integers).
C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0633f959-5e84-4466-98ec-7d9c4e0fb9bf%2Fde9024ce-7e69-42df-b3b0-a01ce4f65d9a%2F05s11ao_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b. Let R be a ring with unity and ICRX R. Prove that I is an ideal of the ring R × R if and
only if I = 11 × I2 for some ideals I1 and I2 of R.
Prove that neither 2 nor 17 are prime elements in Z[i] (the ring of Gaussian integers).
C.
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