課程名稱 |
代數二 ALGEBRA(Ⅱ) |
開課學期 |
96-2 |
授課對象 |
理學院 數學系 |
授課教師 |
李白飛 |
課號 |
MATH7106 |
課程識別碼 |
221 U3840 |
班次 |
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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 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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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.
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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 |
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Office Hours |
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指定閱讀 |
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參考書目 |
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評量方式 (僅供參考) |
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