Euclidean rings, Gauss integers. Factorial rings, Eisenstein’s criterion, Gauss’s lemma. Symmetric polynomials, Newton’s algorithm. Resultant, Bezout’s theorem. Modules over principal domains, Jordan canonical form. Hilbert basis theorem. Hilbert zeros theorem. Groups, quotient groups. Lagrange’s theorem. Finite groups with two generators. Groups of permutations. Sylow’s theorem. Jordan-Hölder theorem. Soluble groups.

References:
ARTIN, M. – Algebra. Prentice-Hall, New Jersey, 1991.
GARCIA, A. and LEQUAIN, Y. – Algebra: an introductory course. 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. – Modern Algebra. Vol. I, Lisbon, Portuguese Mathematical Society, 1948.

* Basic syllabus. The teacher has the autonomy to make any changes.