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.