Let R be a commutative ring with unity. Suppose that a is a unit and b is nilpotent. Sho...

Let R be a commutative ring with unity. Suppose that a is a unit and b is nilpotent. Show that a + b is a unit. (Hint: See Exercise 29 in Chapter 12.)

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Suppose that a and b belong to a commutative ring R with unity. If a is a unit of R and b² = 0, show that a + b is a unit of R.