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課程名稱 |
模論(一)
Module Theory (I) |
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開課學期 |
104-1 |
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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 |
MATH5007 |
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課程識別碼 |
221 U6640 |
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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 |
星期一8(15:30~16:20)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/1041MATH5007_ |
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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 |
Modules, Submodules and Factor Modules. Homomorphisms of Modules and Rings. Direct Products, Direct Sums and Free Modules. Injective and Projective Modules. Artinian and Northerian Modules. Local Rings and Krull-Remak-Schmidt Theorem. Semisimple Modules and Rings. Radical and Socle. Tensor Product, Flat Modules and Regular Rings. |
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課程目標 |
This course is intended to provide a reasonably self-contained account of a major portion of the general theory of modules and related rings suitable as an introductory course for more advanced graduate courses. |
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課程要求 |
Undergraduate Algebra. |
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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 |
F. W. Anderson and K. R. Fuller, Rings and Categories of Modules. |
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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 |
9/14,9/17 |
Modules, Submodules. |
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第2週 |
9/21,9/24 |
Factor Modules. Homomorphisms of Modules. |
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第3週 |
9/28,10/01 |
Factorization of Homomorphisms of Modules. |
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第4週 |
10/05,10/08 |
Jordan-Holder Theorem. Dual Modules. |
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第5週 |
10/12,10/15 |
Direct Products, Direct Sums and Free Modules. Artinian and Noetherian Modules. |
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第6週 |
10/19,10/22 |
Endomorphism Rings of Artinian and Noetherian Modules. Krull-Schmidt Theorem. |
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第7週 |
10/26,10/29 |
Local Rings. Modules over Principal Ideal Domains. |
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第8週 |
11/02,11/05 |
Jordan Form. Rational Canonical Form. Semisimple Modules. |
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第9週 |
11/09,11/12 |
Semisimple Rings. Midterm Examination. |
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第10週 |
11/16,11/19 |
Wedderburn-Artin Theorem. |
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第11週 |
11/23,11/26 |
Density Theorem. Free Modules. Projective Modules. |
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第12週 |
11/30,12/03 |
More on Projective Modules. Divisible Groups. Injective Modules. |
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第13週 |
12/07,12/10 |
More on Injective Modules. |
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第14週 |
12/14,12/17 |
Tensor Product. |
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第15週 |
12/21,12/24 |
More on Tensor Product. Adjoint Isomorphism Theorem. |
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第16週 |
12/28,12/31 |
Flat Modules. Character Modules. |
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第17週 |
1/04,1/07 |
Regular Rings. Decomposition of Injective Modules. |
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