MAT 534: Algebra I Fall 2015 | |

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## General Information
- Groups: normal subgroups, quotient groups, Lagrange's theorem, class formula, finite p-groups and solvable groups, Sylow's theorems, finitely generated abelian groups.
- Rings and modules: subrings, fields, prime and maximal ideals, quotient rings, ID's, PID's, UFD's, polynomial rings, field of fractions, the Wedderburn theorem, Hilbert basis theorem, finitely generated modules over a PID.
- Vector spaces: basis, linear maps and matrices, dual spaces, determinants, eigenvalues and eigenvectors, inner products, spectral theorem for normal operators.
Please be aware that there is a number of misprints in the book; you can find the errata here Additional references: - A. Knapp, Basic Algebra, Birkhauser, 2006.
- M. Artin, Algebra, Prentice Hall, 1991.
- S. Lang, Algebra, 3rd ed., Addison-Wesley, 1993.
- Jacobson, Basic Algebra, 2nd ed, W.H. Freeman, New York, 1985, 1989.
- Rotman, Introduction to the Theory of Groups, Springer Verlag.
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