Question: 1. (6 points) Let R be a commutative ring, and let a, b E R. Show that. N ={m+3b | 133 ER} is an ideal

1. (6 points) Let R be a commutative ring, and let a, b E R. Show that. N ={m+3b | 133 ER} is an ideal of R. 2. (5 points) Let R be a ring and F a eld, and suppose o5 : F > R is a ring homomorphism. Show that. either is the zero homomorphism or (35 is one-toone. 8. (6 points) Let. R be a ring and N an ideal of R. Show that R/N is commutative if and only ifrss'r E N for all r, 3 E N

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