Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Which of Examples 1 through 5 are fields?

I EXAMPLE 1 The ring of integers is an integral domain.
I EXAMPLE 2 The ring of Gaussian integers Z[i] = {a + bi | a, b E Z} is
an integral domain.
I EXAMPLE 3 The ring Z[x] of polynomials with integer coefficients is
an integral domain.
I EXAMPLE 4 The ring Z[V2] = {a + bv2 1 a, b E Z} is an integral
domain.
I EXAMPLE 5 The ring Z, of integers modulo a prime p is an integral
domain.
I EXAMPLE 6 The ring Z, of integers modulo n is not an integral domain
when n is not prime.
I EXAMPLE 7 The ring M,(Z) of 2 × 2 matrices over the integers is not
an integral domain.
I EXAMPLE 8 ZOZ is not an integral domain.
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Transcribed Image Text:I EXAMPLE 1 The ring of integers is an integral domain. I EXAMPLE 2 The ring of Gaussian integers Z[i] = {a + bi | a, b E Z} is an integral domain. I EXAMPLE 3 The ring Z[x] of polynomials with integer coefficients is an integral domain. I EXAMPLE 4 The ring Z[V2] = {a + bv2 1 a, b E Z} is an integral domain. I EXAMPLE 5 The ring Z, of integers modulo a prime p is an integral domain. I EXAMPLE 6 The ring Z, of integers modulo n is not an integral domain when n is not prime. I EXAMPLE 7 The ring M,(Z) of 2 × 2 matrices over the integers is not an integral domain. I EXAMPLE 8 ZOZ is not an integral domain.
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