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A characterization of division rings in terms of an equation concerning its elem

Source: Romanian NO 2011, grade xii, p.3

October 3, 2019
abstract algebraRing Theory

Problem Statement

The equation xn+1+x=0 x^{n+1} +x=0 admits 0 0 and 1 1 as its unique solutions in a ring of order n≥2. n\ge 2. Prove that this ring is a skew field.
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