Let R = ℤ/3ℤ, the integers mod 3. The ring of Gaussian integers mod 3 is defined by R[i] = { a + bi : a, b ∈ ℤ/3ℤ and ? = √−1 }. Show that R[i] is a field.

Q: Let n > 2 be an integer. Show that Z/Zn is a field if and only if n is a prime number.

A: Let A=1¯,2¯,3¯,...,n-1¯ we show for ⇒ Let ℤℤn is a field⇒∀a∈A,∃x∈A such that ax=1¯ax≡1modn has a…

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Q: Let F = {0, 1,2} denote the field of 3 elements. Consider the field K obtained by adjoining the…

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Q: Let R = Z/3Z, the integers mod 3. The ring of Gaussian integers mod 3 is defined by R[i] = { a + bi…

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Q: Appendix C: Fields Problem 1. Consider the following set of complex numbers Q(i) = (a + bi: a, b €…

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Q: Let Z3[i] = {a + bi : a, b ∈ Z3, i2 = −1} where arithmetic is done mod 3. 1.  Is Z3[i] an integral…

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Q: Consider Z4[i] = (a + bi: a, b € Z4), the ring of Gaussian integers modulo How many elements does…

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