Assume that F is a field. (a) What properties does F satisfy for addition? b) What properties does F satisfy for multiplication? Which of the following are fields? Explain. (a) Z (b) Q (c) R (d) C (e) Z, (f) Ze (g) Z7 (h) Z8 (i) Z2 x Z2

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

A: The elements areNote: the elements of  are

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A: Let F be a field. We have to prove that (-1)·x=-x.

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Q: 9. The field (Q, +,.) can be embedded in the field... (a) (Q, +,.) (b) (R, +,.) (c) (C, +,.) (d) All…

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Q: Suppose that F is a field of order 125 and F* = (a). Show that a62 = −1. Solution: Narrative:

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Q: (6) The ring (Z,2, +12, 12) is .. ..... (а) field (b) semi-simple (c) simple (d) No Choice

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