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Why is Z/2Z a field, when Z is not?
Hello ,
Can someone explain why Z/2Z is a field. I thought Z/2Z represented the even integers. Therefore, I'm not sure why Z/2Z is a field if the elements are not invertible?!!
Can someone explain why Z/2Z is a field. I thought Z/2Z represented the even integers. Therefore, I'm not sure why Z/2Z is a field if the elements are not invertible?!!
beast
Hello ,
Can someone explain why Z/2Z is a field. I thought Z/2Z represented the even integers. Therefore, I'm not sure why Z/2Z is a field if the elements are not invertible?!!
Can someone explain why Z/2Z is a field. I thought Z/2Z represented the even integers. Therefore, I'm not sure why Z/2Z is a field if the elements are not invertible?!!
2Z is the set of even integers
Z/2Z or Z2 is a field with two elements - you can think of them as Even and Odd if you want, or 0 and 1. Their rules of adding and multiplying are
E+E=E, E+O=O, O+O=E
EE = E, EO=E, OO=O
The additive identity is E, the multiplicative identity is O, and O's inverse is O.
Neapolitan
2Z is the set of even integers
Z/2Z or Z2 is a field with two elements - you can think of them as Even and Odd if you want, or 0 and 1. Their rules of adding and multiplying are
E+E=E, E+O=O, O+O=E
EE = E, EO=E, OO=O
The additive identity is E, the multiplicative identity is O, and O's inverse is O.
Z/2Z or Z2 is a field with two elements - you can think of them as Even and Odd if you want, or 0 and 1. Their rules of adding and multiplying are
E+E=E, E+O=O, O+O=E
EE = E, EO=E, OO=O
The additive identity is E, the multiplicative identity is O, and O's inverse is O.
Thanks again, you've been a great help! I wish you were my lecturer!
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