Chapter 14

Exercise 1. This software determines the number of elements in the ring Z[i]/<a + bi> (where i² = -1). Run the program for several cases and formulate a conjecture based on your data.

Exercise 2. This software determines the characteristic of the ring Z[i]/<a + bi> (where i² = -1). Run the program for several cases and formulate a conjecture based on your data.

Exercise 3. This software determines when the ring Z[i]/<a + bi> (where i² = -1) is isomorphic to the ring Z_{a² + b²}. Run the program for several cases and formulate a conjecture based on your data.

 

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