Well, write all the conditions for the set of symbols to form a field. For example, taking into account that with prime is a field, then. given then,
etc, etc,... . Show your work and we check it.
Hi all, I am going through a Algebra textbook and I need a bit of help with this question, so thank you in advance for any help.
Question: Prove that the set of symbols forms a field with nine elements, if the laws of composition are made to mimic addition and multiplication of complex numbers. Will the same method work for ? For ? Explain.
So I can see that the nine elements are: but I am confused as to where to go from here.
June
Thanks FernandoRevilla, sorry for my late reply, been gone a few days.
So,
Addition and Multiplication:
and
Inverse:
Distributive:
The complex addition identity is 0.
The complex multiplication identity is 1.
And commutative and associative follow easily.
Is this correct working out?
Thanks
So I need to look at and to see if they form a field, if the laws of composition are made to mimic addition and multiplication of complex numbers.
So for the elements are:
So where do I go from here?
Any help guys?
Thanks