Let x and y belong to a commutative ring R with prime

Chapter 13, Problem 49E

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Problem 49E

Let x and y belong to a commutative ring R with prime characteristic p.

a. Show that (x + y) p = xp + yp.

b. Show that, for all positive integers n, (x + y) pn = xpn + ypn.

c. Find elements x and y in a ring of characteristic 4 such that (x + y)4 ≠ x4 + y4. (This exercise is referred to in Chapter 20.)

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