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

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

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 18E

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Question

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
(d) C
(e) Z5
(f) Z6
(g) Z7
(b) Q
(с) R
(h) Zs
(i) Z2 x Z2

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