Ring theory-nil radical, Let R be a ring with the property

Ring theory-nil radical

Reference no: EM13126524

Let R be a ring with the property that every element is either nilpotent or invertible. If a, b, c are in R with a and b nilpotent, show that ac, ca, and a + b are nilpotent. For the latter, first observe that a + b cannot equal 1. Conclude that Nil (R) is the set of all nilpotent elements of R.

(nil radical Nil (R) is defined to be the sum of all nil two-sided ideals of R)

Reference no: EM13126524

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