= Recall, Z2 {0, 1}. Consider Z2 [i] = {a+bi: a,b Z2} with addition and multiplication....

 

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= Recall, Z2 {0, 1}. Consider Z2 [i] = {a+bi: a,b Z2} with addition and multiplication. The coeffici are reduced modulo 2. So, the elements in Z2[i] are Z2[i]={0, 1, 1, 1+i} 1. Construct a multiplication table for Z2[i]. 2. Give a reason why this is or is not an integral domain. 3. Give a reason why this is or is not a field. = Recall, Z2 {0, 1}. Consider Z2 [i] = {a+bi: a,b Z2} with addition and multiplication. The coeffici are reduced modulo 2. So, the elements in Z2[i] are Z2[i]={0, 1, 1, 1+i} 1. Construct a multiplication table for Z2[i]. 2. Give a reason why this is or is not an integral domain. 3. Give a reason why this is or is not a field.