COVERED MATERIAL
Updated Fri, Mar 22, 1996
Algebra 464. Fall 1996.
Michael Boshernitzan.
- pages 345-373, 389-409, 492-515, 527-530
- Chapter 10, Section 5 - independent reading.
- Classification of rings of orders 2,3,5,6,7,10,11,14,15,...
- Finite (dimensional) extensions integral domain (which must be fields)
over R, C and Q.
- THEOREM: arctan(x)/pi is irrational where x>0 is ratioanal and not 1.
The fact that Z[i] is UFD and the classification of Gaussian primes are used in the proof.
- Proved that there are infinitely many primes of the form 4k+3 and 4k+1.
- Factorization in Polynomial Ring. Gauss Lemma. Eisenstein Criterion.
- Fields extensions. Constructions with Ruler and Compass. Finite Fields.
