Possibly the most interesting part of this section is the latter half which deals with Homomorphisms.

## Theorem 6.12: First Isomorphism Theorem

Let be a surjective isomorphism of rings with kernel

K. Then the quotient ringR/Kis isomorphic toS.

If I understand this correctly then when comparing this to data transfer *f* represents the transfer of data from *R* to *S* where *K* is the amount of lost data. Looking at the kernel in Example 4 () we can say that of the data is lost during the transfer.