(a) If R is the ring of all 2 X 2 matrices over Z, then for any...
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(a) If R is the ring of all 2 X 2 matrices over Z, then for any A ϵ R, (x + A)(x - A) = x2 - A2 ϵ R[x].
(b) There exist C,A ϵ R such that (C + A)(C - A) ≠ C2 - A2• Therefore, Corollary 5.6 is false if the rings involved are not commutative.
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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