Commutative algebra [ LMAT1331 ]

The course is in two parts. The technique of Gröbner bases and the fundamentals of elimination theory are discussed in the first part, which culminates with the proof of Hilbert's Nullstellensatz. The second part is centered on the theory of finitely generated modules over a principal ideal domain. Their structure is determined, and the result is applied to the Jordan canonical form of linear operators.

The evaluation consists of a written examination, which includes theoretical problems and explicit computations.

Classroom sessions mix theoretical explanations and problems, some of which require the use of a computer.

The discussion is loosely based on the following monograph:
 Cox, David; Little, John; O'Shea, Donal:  "Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra." Third edition. Undergraduate Texts in Mathematics. Springer, New York, 2007. xvi+551 pp. ISBN: 978-0-387-35650-1; 0-387-35650-9