From what I understand, fields, as far as numbers Zeta are concerned, are zeta in some prime number. I can't seem to figure out why.
Also, an inverse of the product for any number in the ring is another number or itself that can be multiplied with it and yield 1. In a field, all the numbers have an inverse, but in zeta 6 (for example), which is not a field the only numbers that have an inverse are 1 and 5, in this case being themselves. Not sure I got everything down. What are these numbers called, btw? I am studying abroad in Spain, and in Spanish they are "unidades" but I don't know what they are in English.
It's not required of me to understand why the only fields are of prime numbers in zeta though, so I think I am alright. But am I right about units of a non-field being multiplicate inverses?
Originally Posted by HeadOnAPike
You mean "...units of a non field HAVING multiplicative inverses"? Yes, this is right: a unit in a ring is an element u s.t. uv=1 for some element v in the ring.