代數通論一   (89年度 上學期)

Permutation Groups. Finite Direct Product of Groups. The Sylow Thorems. Normal and Subnormal Series. Group Extensions. Some Simple Groups. Free Modules. Modules over a Principal Ideal Domain. Algebras. Simple and Primitive Rings. Jacobson Density Theorem. Prime and Semeiprime Rings. Wedderburn-Artin Structure Theorem. Semisimple Modules. The Brauer Group. Some Classic Theorems on Simple Algebras.

(1) Thomas W. Hungerford, "Algebra". (2) I. N. Herstein, "Noncommutative Rings". (3) N. Jacobson, "Basic Algebra, I, II". (4) Joseph J. Rotman, "The Theory of Groups, An Introduction".

以學期考試成績占70%，習題成績占30%為原則

為期與本系另一課程"體論"相輔相成,本課程內容除Zorn's Lemma, Tensor Product 以及Transcendental Basis等題材外，將盡量避免與該課程重疊。