|
課程名稱 |
代數二
ALGEBRA(Ⅱ) |
|
開課學期 |
96-2 |
|
授課對象 |
理學院 數學研究所 |
|
授課教師 |
李白飛 |
|
課號 |
MATH7106 |
|
課程識別碼 |
221 U3840 |
|
班次 |
|
|
學分 |
3 |
|
全/半年 |
半年 |
|
必/選修 |
選修 |
|
上課時間 |
星期二3,4(10:20~12:10)星期四3(10:20~11:10) |
|
上課地點 |
舊數103舊數103 |
|
備註 |
Course prerequisite：ALGEBRA(I)
總人數上限：30人 |
|
|
|
|
課程簡介影片 |
|
|
核心能力關聯 |
核心能力與課程規劃關聯圖 |
|
課程大綱
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
課程概述 |
Contents：
Fields: Field Extensions. The Fundamental Theorem of Galois Theory. Splitting Fields, Algebraic Closure and Normality. The Galois Group of a Polynomial. Finite Fields. Separability. Cyclic Extensions. Cyclotomic Extensions. Radical Extensions. Transcendence Bases. Linear Disjointness and Separability.
Commutative Rings: Chain Conditions. Prime and Primary Ideals. Primary Decomposition. Noetherian
Rings and Modules. The Hilbert Nullstellensatz.
Noncommutative Rings: Simple and Primitive Rings. The Jacobson Radical. Semisimple Rings. The Prime Radical, Prime and Semiprime Rings. Algebras. Division Algebras.
|
|
課程目標 |
Course Goal：A deeper survey of basic notions in algebra, possibly required in other graduate courses. |
|
課程要求 |
Course prerequisite：ALGEBRA(I)
III.Reference material ( textbook(s) )：
Thomas W. Hungerford, “Algebra”.
Nathan Jacobson, “Basic Algebra II”.
Joachim Lambek, “Lectures on Rings and Modules”.
Paul J. McCarthy, “Algebraic Extensions of Fields”.
IV.Grading scheme：
Midterm and Final Examinations, 50% each. |
|
預期每週課後學習時數 |
|
|
Office Hours |
|
|
指定閱讀 |
|
|
參考書目 |
|
|
評量方式
(僅供參考) |
|
|