Topics in Modern Algebra
Examines the algebra of various mathematical structures with the goal of gaining a broader and more sophisticated understanding of algebraic structures. Topics include groups, rings, fields and other main algebraic structures.
- Construct and evaluate finite and infinite fields.
- Apply main properties of vector spaces for construction of extension fields, elaborate algebraic extensions.
- Elaborate main properties of rings, subrings, ideals and quotient rings, rings of polynomials and formal power series, division in rings.
- Extend group structure to finite permutation groups (Cayley’s Theorem).
- Prove Sylow’s Theorems for finite groups.
- Generate groups given specific conditions.
- Elaborate the Fundamental Theorem of Galois Theory.
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