B. In Exercises 5-8, each element of the given congruence-class ring can be written in the...

 

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B. In Exercises 5-8, each element of the given congruence-class ring can be written in the form [ax + b] (Why?). Determine the rules for addition and multiplication of congruence classes. (In other words, if the product [ax + b][cx + d] is the class [rx + s], describe how to find r and s from a, b, c, d, and similarly for addition.) 5. R[x]/(x + 1) [Hint: See Example 1.] 6. Q[x]/(x²-2) 7. Q[x]/(x²-3) 0 Show that If...1/1.2 8. Q[x]/(x²) B. In Exercises 5-8, each element of the given congruence-class ring can be written in the form [ax + b] (Why?). Determine the rules for addition and multiplication of congruence classes. (In other words, if the product [ax + b][cx + d] is the class [rx + s], describe how to find r and s from a, b, c, d, and similarly for addition.) 5. R[x]/(x + 1) [Hint: See Example 1.] 6. Q[x]/(x²-2) 7. Q[x]/(x²-3) 0 Show that If...1/1.2 8. Q[x]/(x²)

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The ring Qx has elements of the form px where p has all coeffi... View the full answer