MTL105: Difference between revisions
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== MTL105 : Algebra == | == MTL105 : Algebra == | ||
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. | 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. | ||
Latest revision as of 16:42, 14 April 2026
| MTL105 | |
|---|---|
| Algebra | |
| Credits | 3 |
| Structure | 3-0-0 |
| Pre-requisites | |
| Overlaps | MTL501 |
MTL105 : Algebra
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.