Which of the following sets are subrings of the field R of real numbers? (a) A = {m+n√√2 | m, n = Z and n is even} (b) B = {m+n√√2 | m, n = Z and m is odd} (c) C = {a+b√√2 | a, b = Q} (d) D = {a+b√√/3 + c39 | a, b, c = Q} C (e) E = {m+nu | m, n = Z}, where u = (1+√√3)/2 (f) F = {m + nv | m, n = Z}, where v = (1 + √5)/2

Q: If R= = b {(6) a. b. c real} and 1-{(5) b real). | a, I = (a) R is a ring. (b) I is an ideal of R.…

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Q: b) If p(x) = x² + x³ + x² + x + 1, and g(x) = x² + x¹ + x² + 1, what is p(x)/q(x)?

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Q: a) The ring R[x, y]/(x + 1) is a field. b) The ring Z[x]/(7) is a principal ideal domain

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Q: (b) How many elements are there in S? Justify your answer.

A: The elements areNote: the elements of  are

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Q: Find the inverse of 6 − 5√7 in the field ℚ[ √7]

A: To find the inverse of 6 − 5√7 in the field ℚ[ √7].

Q: .4 Find the splitting field of x¹ + x² + 1 over

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