In the lecture 25.3 I ¡­

In the lecture 25.3 I did not explain the proofs of theorems 20.12 in section 20 and the details of the construction of a quotient field. I encourage you to red them carefully on your own. In the lecture 8.4 I will discuss factor rings (sections 26,27) and start the discussion of polynomials over a field (section 22).