MA 314: Topics in Commutative Algebra
Credits: 3:0
Abstract relations and Dickson’s Lemma; Hilbert Basis theorem, Buchberger Criterion for Grobner Bases and Elimination Theorem; Field Extensions and the Hilbert Nullstellensatz; Decomposition, Radical, and Zeroes of Ideals; Syzygies, Grobner Bases for Modules, Computation of Hom, Free Resolutions; Universal Grobner Bases and Toric Ideals.
Suggested books and references:
- T. Becker and V. Weispfenning, Grobner Bases–a Computational Approach to Commutative Algebra, Springer 1993.
- W.W. Adams and P. Loustaunau, An Introduction to Grobner Bases, Graduate Studies in Mathematics, Vol. 3, American Mathematical Society, 1994.
- B. Sturmfels, Grobner bases and convex polytopes, American Mathematical Society 1996.