Math 515 homework #15 Due date: 19980401 D. J. Bernstein 19980325 Exercise 41. Let p be an element of a ring R. Let I be an ideal of R contained in pR. Define J = {x ∈ R : px ∈ I}. Prove that J is an ideal of R with pJ = I. Exercise 42. Eisenbud 9.1(a). Exercise 43. Eisenbud 9.1(b). Exercise 44. Eisenbud 9.2(a). Exercise 45. Eisenbud 9.2(b).