Question: 1. (6 points) Let R be a commutative ring, and let {1,6 6 R. Show that. N={ra+3b | 133612} is an ideal of R. 4.

1. (6 points) Let R be a commutative ring, and let {1,6 6 R. Show that. N={ra+3b | 133612} is an ideal of R. 4. Let 9(3) 2 m3 + 1, and let G be the polynomial code of length 8 generated by 9(a). (a) (3 points) Is 0 cyclic? (b) (3 points) How many code words are in C? (c) (2 points) What is the transmission rate of C? 5. (a) (4 points) Find a maximal ideal of Q[:1:]. (b) (4 bonus points) Find a prime ideal of Q[:I:] that is not maximal. (c) (4 bonus points) Find a proper ideal of Q[a:] that is not prime

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