Syllabus
1. Divisibility in commutative cancellative monoids.
2. Principal ideal and Euclidean domains. Polynomial rings, multiplicity of roots, evaluation homomorphism. Why all finite multiplicative subgroups of fields are cyclic.
3. Splitting fields of a polynomial. Rupture field of a polynomial.
4. Finite fields. Existence of irreducible polynomials over finite fields.
5. Free algebras, terms and varieties.
Annotation
The second part of course in basic algebra is concerned with divisibilty in commmutative domains, extensions of fields and basic properties of the notion variety.