MTL105: Algebra

3 Credits (3-0-0)

Overlaps with: MTL501

Preliminaries: Equivalence relations and partitions. Groups: Subgroups, Cyclic groups, Abelian groups, permutation groups; Langrange’s theorem, normal subgroups, quotient groups, isomorphism theorems. Direct product of groups, structure theorem of finitely generated abelian groups, Sylow’s theorems and applications. Rings: Definition and examples, units and zero divisors. Ideals and quotients, principal ideals, prime ideals, maximal ideals, integral domain, PID, Euclidean domain, UFD. Modules over a commutative ring with unity: Free module, quotient module, exact sequences. Fields: Finite fields, field extensions, splitting fields.