Abstract Algebra Qualifying Exam Syllabus
Kent Sate University
Department of Mathematical
Sciences
Groups
Including homomorphism theorems, permutation groups, automorphisms, finitely
generated abelian groups, products of groups, group actions, Sylow theorems,
pgroups, nilpotent groups, solvable groups, normal and subnormal series,
JordanHolder Theorem, special subgroups (e.g. commutator subgroup, Frattini
subgroup, etc.).
Rings
Including matrix rings, polynomial rings, factor rings, endomorphism rings,
rings of fractions, localization and local rings, prime ideals, maximal
ideals, primary ideals, integral domains, Euclidean domains, principal
ideal rings, unique factorization domains, Jacobson radical, chain conditions,
modules, factor modules, irreducible modules, Artinian and Noetherian rings
and modules, semisimplicity.
Fields
Including algebraic extensions, algebraic closures, normal extensions and
splitting fields, separable and purely inseparable extensions, theorem
of the primitive element, Galois theory, finite fields, cyclotomic extensions,
cyclic extensions, radical extensions and solvability by radicals, transcendental
extensions.
Linear Algebra
Including matrix theory, eigenvalues and eigenvectors, characteristic and
minimal polynomials, diagonalization, canonical forms, linear transformations,
vector spaces, bilinear forms, inner products, inner product spaces, duality,
tensors.
Suggested References

D. Dummit and R. Foote  Abstract Algebra

I.M. Isaacs  Algebra  A Graduate Course

T. Hungerford  Algebra

N. Jacobson  Lectures in Abstract Algebra, Vols. I, II, III

N. Jacobson  Basic Algebra I and II

MacLane and Birkhoff  Algebra

S. Lang  Algebra

M. Hall  The Theory of Groups

J. Rose  A Course on Group Theory

J. Rotman  The Theory of Groups, An Introduction

E. Artin  Galois Theory

Hoffman and Kunze  Linear Algebra
This document is also available as a PDF file.
Donald White
white@math.kent.edu