Abstract
Let K = {0, 1,a, b} be a field with four elements. Its characteristic being 2 (a prime number dividing 4) we obtain 1 + 1 = a + a = b + b = 0. The group (K, +) being of Klein type we also have a + b = 1. The inveerse of a must be b. Indeed, a-1 = 1 would imply a = 1, a -1 = a would imply a 2 = 1 and (a - 1)2 = 0 (char(K) = 2) and hence a = 1. So a-1 = b or ab = 1 and even a(1 + a) = 1 or a 2 =1 + a. An isomorphism to K 4 (from 1.9) is now obviously defined
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© 1998 Springer Science+Business Media Dordrecht
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Cǎlugǎreanu, G., Hamburg, P. (1998). Division Rings. In: Exercises in Basic Ring Theory. Kluwer Texts in the Mathematical Sciences, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9004-4_24
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DOI: https://doi.org/10.1007/978-94-015-9004-4_24
Publisher Name: Springer, Dordrecht
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