19. Assume (R, +,) is a ring with the property that a² + a E cent R for every element a in R. Show that (R, +, ) is a commutative ring. [Hint: Make use of the expression (a + b)2 + (a + b) to prove,...

Extracted text: 19. Assume (R, +,) is a ring with the property that a² + a E cent R for every element a in R. Show that (R, +, ) is a commutative ring. [Hint: Make use of the expression (a + b)2 + (a + b) to prove, first, that a . b+b.a lies in the center.) 20. Illustrate Theorem 3-18 by considering the rings (Zo, +o, e), (Z3, +3, a), and the homomorphism f: Ze - Za defined by f(0) = f(3) = 0, (1) = 1(4) = 1, S(2) - S(5) = 2. %3D %3D %3D