Algebra I

Euclidean Rings, Gaussian Integers. Factorial Rings, Eisenstein’s Criterion, Gauss Lemma. Symmetric Polynomials, Newton’s Algorithm. Resultant. Bezout’s Theorem. Modules over Principal Ideal Domains, Jordan’s Canonical Form. Hilbert’s Base Theorem. Hilbert’s Zero Theorem. Groups, Quotient Groups. Lagrange’s Theorem. Finite Groups With Two Generators. Permutation Groups. Sylow’s Theorem. Jordan-Hölder Theorem. Solvable Groups.

References:
ARTIN, M. – Algebra. Prentice-Hall, New Jersey, 1991.
GARCIA, A. and LEQUAIN, Y. – Álgebra: um curso de Introdução. Rio de Janeiro, IMPA, Projeto Euclides, 1988.
JACOBSON, N. – Lectures in Abstract Algebra, Vol. I, Van Nostrand, New York, 1951.
VAN DER WAERDEN, B. L. – Álgebra Moderna. Vol. I, Lisboa, Sociedade Portuguesa de Matemática, 1948.