- Understand central relationships about groups, rings, fields;
- Derive and prove simple consequences of classical theorems independently;
- Investigate properties of given algebraic structures;
- Construct algebraic structures with given properties
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Groups (factor groups, isomorphism theorems, cyclic groups, direct products), Rings (isomorphism theorems, localization and quotient field, unique factorization domains, principal ideal domains, euclidian rings, divisibility theory), Fields (subfield lattice, field extensions, splitting fields, algebraic closure)
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