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課程名稱 |
模論(二)
Module Theory II |
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開課學期 |
104-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
李白飛 |
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課號 |
MATH5030 |
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課程識別碼 |
221 U6870 |
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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 |
星期二1(8:10~9:00)星期四3,4(10:20~12:10) |
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上課地點 |
天數430天數430 |
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備註 |
總人數上限：10人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1042MATH5030_ |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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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 |
Categories and Functors. Products and Coproducts. Direct and Inverse Limits. Generators and Cogenerators.Pushout and Pullback. Small Submodules. Projective Covers. Radical and Socle. Semiperfect Modules and Perfect Rings. Rings with Perfect Duality. Quasi-Frobenius Rings. |
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課程目標 |
This course is a continuation of the course MATH 5007, an introductory course on modules and related rings suitable for graduate and advanced undergraduate students. |
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課程要求 |
MATH 5007. |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
F. Kasch, "Modules and Rings". |
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參考書目 |
J. J. Rotman, "Notes on Homological Algebra". |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Midterm Examination |
50% |
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2. |
Final Examination |
50% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/22,2/25 |
Review. Categories. Functors. |
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第2週 |
3/03 |
Funtor Morphisms and Adjoint Functors. Products. |
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第3週 |
3/07,3/10 |
Coproducts. Direct Limits. |
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第4週 |
3/14,3/17 |
Inverse Limits. Pushouts and Pullbacks. Generators and Cogenerators. |
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第5週 |
3/21,3/24 |
Characterizations of Generators and Cogenerators. Direct Sum of Injective Modules over Noetherian Rings. |
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第6週 |
3/28,3/31 |
Decomposition of Injective Modules over Noetherian Rings. Superfluous Submodules. Radical and Socle. |
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第7週 |
4/07 |
Further Properties of Radical. |
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第8週 |
4/11,4/14 |
Radical of a Ring. Characterizations of Finitely Generated and Finitely Cogegenerated Modules. Characterizations of Artinian Rings and Noetherian Rings. |
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第9週 |
4/18,4/21 |
The Radical of the Endomorphism Ring of an Injective or Projective Module. Addition Complemet. Projective Cover. |
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第10週 |
4/25,4/28 |
Midterm Examination. Semiperfect Modules. |
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第11週 |
5/02,5/05 |
Lifting of Direct Decompositions. Projective Semiperfect Modules. |
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第12週 |
5/09,5/12 |
More on Projective Semiperfect Modules. Indecomposable Semiperfect Modules. Nil and T-Nilpotent Ideals. |
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第13週 |
5/16,5/19 |
Perfect Rings. Dual modules. |
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第14週 |
5/23,5/26 |
Duality Properties. Annihilator Properties. Injectivity and Cogenerator Properties.. |
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第15週 |
5/30,6/02 |
Rings with Perfect Duality. |
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第16週 |
6/06 |
Quasi-Frobenuius Rings. |
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第17週 |
6/13,6/16 |
More on Quasi-Frobenuius Rings. |
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