I am trying to get a full understanding of Cohn Example 4 on page 9 - see attachment.

A formal and rigorous example showing clearly the nature and role of the families (and their indicies) involved would help enormously.

Cohn, page 9, Example 4 states:

"Let I be any set and denote by the set of all functions from I to Z.

Thus the elements of are families of integers indexed by I.

Addition and multiplication are defined componentwise:

where

and where

It is very easily verified becomes a ring."

In order to understand this example fully, I would very much appreciate an example of what is at work here showing clearly the nature of the families and their indices.

Peter