Let be a prime ideal, be a commutative ring with identity, . Then will be a multiplicative subset of , that is,
Define as the set .
we may write as
define the add operation
define the times operation
Then we can prove that is a commutative ring of identity.
Prove that has a unique maximal ideal..
I have thought of the same ..but i do it in another way and it seems that it is impossible...
a theorem says is a maximal field in iff is a field.
but i cannot find the "1" in the
if is the "1", then
it requires that
so it requires is alway in , right?
so ,but , that implies ........So I am confused..
Is there any mistake??