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課程名稱 |
代數二
Algebra (Ⅱ) |
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開課學期 |
103-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
康明昌 |
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課號 |
MATH7106 |
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課程識別碼 |
221 U3840 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一3,4(10:20~12:10)星期四7,8(14:20~16:20) |
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上課地點 |
天數102天數102 |
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備註 |
研究所數學組基礎課。先修知識:代數導論。
總人數上限：30人
外系人數限制：5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 |
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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 |
Rings and Modules: Exact Sequences. Projective and Injective Modules. Hom and Duality. Tensor Products. Algebras.
Fields: Field Extensions. The Fundamental Theorem. Splitting Fields, Algebraic Closure and Normality. The Galois Groups of a Polynomial. Finite Fields. Separability. Cyclic Extensions. Radical Extensions. Transcendental Bases.
Linear Algebra: Determinants. Decomposition of a Single Linear Transformation and Similarity.
Commutative Rings: Prime and Primary Ideals. Primary Decoposition. Noetherian Rings and Modules. Ring Extensions. Dedekind Domains. The Hilbert Nullstellensatz.
Non-Commutative Rings: Simple and Primitive Rings. The Jacobson Radical. Semisimple Rings. Algebras. Division Algebras. |
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課程目標 |
A deeper survey of basic notions in algebra, possibly required in other graduate courses. |
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課程要求 |
建議先修 ALGEBRA (I) MATH 7105.
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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 |
Nathan Jacobson, "Basic Algebra II".
Oscar Zariski and Pierre Samuel, "Commutative Algebra I". |
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評量方式
(僅供參考) |
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