Question

7.3.4. The goal of this problem is to compare and contrast two different rings Ri and R2. (a) Suppose R F2]/(mx)), where m(x) is a polynomial of degree 2 in F2[r]. How (b) Now let Ři-P2[aj, where αι is a root ofz? + i, and let R2ーF2[a], where a2 is a many elements does R have? Briefly explain. (See Theorem 7.3.2.) root of 2 +1. Make multiplication tables for each of R1 and R2, using reduced representations for all elements (c) For i = 1, 2, answer the following questions: Does have zero divisors? How many units are there in R?

Answer 1

2 le noton asGn) in f2 el men

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