Algebra MAT2400

Course content:

Semigroups, monoids, groups. Transformation groups and permutation groups. Homomorphisms, isomorphisms and automorphisms of groups. Cayley's theorem and Lagrange's theorem. Cyclic groups. Normal subgroups and factor groups. Isomorphism theorem. Commutator subgroup. Characterization of finitely generated abelian groups. Sylow theorems. Ring, subring. Ideals and factor rings. Factorization in R[x]. Euclidean rings. Unique factorization domains. Fields. Fields of quotients. Field extensions. Algebraically closed fields. Algebraic analysis of ruler-and-compass constructions.

Learning outcomes: the ability to recognize a group (ring, field) structure in algebraic objects; the ability to formulate results of the elementary number theory in terms of groups and rings