Are Algebraic Extensions Always Finite?

[ehrenfest]

How? Can you come up with an example?

The dot notation is definitely not always compatible with field notation, as I will show. Consider the field Z/3Z. Writing 5*2 is absurd because 5 is not an element of the field Z/3Z. You need to write $5 \cdot 2$ if you want to represent the sum $2+2+2+2+2$.

morphism, if you are saying that if F is a field that contains f, then $n \cdot f = nf$ WHEN the characteristic of F is greater than n or equal to 0, then I think that is true.

 

[Hurkyl]

Writing 5*2 is absurd because 5 is not an element of the field Z/3Z.[/itex]

Er, yes it is. 5 denotes the same element that 2 does.

 

[ehrenfest]

OK. This is getting really technical. I would rather move on.