交換代數二   (91年度 下學期)

介紹交換代數的基本概念：primary decomposition of finite modules, Hilbert-Samuel polynomials, dimension theory, Hilbert Nullstellensatz, Hilbert syzygy theorem, regular local rings, Serre's multiplicity.

Serre, Algebre Local Multiplicites, Springer LNM vol 11; 補充教材：Zariski and Samuel, Commutative Algebra, vol.2

期末考筆試或講解論文，由學生任選其一。講解論文以下三篇論文為根據： (1) Roberts, Gabber's proof of the non-negativity conjecture, l'Enseigment Math. 44 (1998) 305~324. (2) Auslander and Buchsbaum, Homological dimension in local rings, Trans. Ama. Math. Svc. 85 (1957) 390~405. (3) Auslander and Buchsbaum, Codimension and multiplicity, Ann. Math. 68 (1958) 625~657.