SUMMARY
The discussion centers on determining the finite field order of Z[i]/A where A=<1+i> in Z[i]. It is established that Z[i]/A is indeed a finite field. The order of this field can be calculated by recognizing that the ideal generated by A corresponds to the norm of the generator, which is 2. Therefore, the order of the finite field Z[i]/A is 2.
PREREQUISITES
- Understanding of Gaussian integers (Z[i])
- Knowledge of ideals in ring theory
- Familiarity with field theory and finite fields
- Basic concepts of norms in algebraic structures
NEXT STEPS
- Study the properties of Gaussian integers and their applications
- Learn about ideals and quotient rings in ring theory
- Explore finite fields and their construction methods
- Investigate the concept of norms in algebraic number theory
USEFUL FOR
Mathematics students, algebra enthusiasts, and anyone studying abstract algebra or number theory will benefit from this discussion.