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Ring Theory Problem Set 1 { Solutions be a ring with unity ...
sites.math.washington.eduRing Theory Problem Set 1 { Solutions Problem 16.1 Let Rbe a ring with unity 1. Show that ( 1)a= afor all a2R. SOLUTION: We have 1+( 1) = 0 by de nition. Multiplying that equation on the right by a, we obtain 1 + ( 1) a = 0 a = 0 by theorem 16.1, part i. By the distributive law, we obtain the equation 1 a+ ( 1) a = 0 and therefore we have a+( 1 ...