模與環講義 [Lectures on Modules and Rings] 下載 mobi epub pdf 電子書 2024

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內容簡介

《模與環講義》主要內容包括：Free Modules， Projective， and Injective Modules、Flat Modules and Homological Dimensions、More Theory of Modules、Rings of Quotients、More Rings of Quotients、Frobenius and Quasi-Frobenius Rings、Matrix Rings， Categories of Modules， and Morita Theory等七大章。

內頁插圖

目錄

Preface
Notes to the Reader
Partial List of Notations
Partial List of Abbreviations

1 Free Modules， Projective， and Injective Modules
1. Free Modules
1A. Invariant Basis Number （IBN）
1B. Stable Finiteness
1C. The Rank Condition
1D. The Strong Rank Condition
1E. Synopsis
Exercises for 1
2. Projective Modules
2A. Basic Definitions and Examples
2B. Dual Basis Lemma and Inveriible Modules
2C. Invertible Fraaional Ideals
2D. The Picard Group of a Commutative Ring
2E. Hereditary and Semihereditary Rings
2F. Chase Small Examples
2G. Hereditary Artinian Rings
2H. Trace Ideals
Exercises for 2
3. Injective Modules
3A. Baer's Test for Injectivitv
3B. Self-Iniective Rings
3C. Injectivity versus Divisibility
3D. Essential Extensions and Injective Hulls
3E. Injectives over Right Noetherian Rings
3F. Indecomposable Injectives and Uniform Modules
3G. Injectives over Some Artinian Rings
3H. Simple Injcctives
3I. Matlis' Theory
3J. Some Computations oflnjective Hulls
3K. Applications to Chain Conditions
Exercises for 3

2 Flat Modules and Homological Dimensions
4. Flat and Faithfully Flat Modules
4A. Basic Properties and Flatness Tests
4B. Flatness， Torsion-Freeness， and von Neumann Regularity
4C. More Flatness Tests
4D. Finitely Presented （f.p.） Modules
4E. Finitely Generated Flat Modules
4F. Direct Products of Flat Modules
4G. Coherent Modules and Coherent Rings
4H. Semihereditary Rings Revisited
4I. Faithfully Flat Modules
4J. Pure Exact Sequences
Exercises for 4
5. Homological Dimensions
5A. Schanuel's Lemma and Projective Dimensions
5B. Change of Rings
5C. Injectivc Dimensions
5D. Weak Dimensions of Rings
5E. Global Dimensions of Semiprimary Rings
5F. Global Dimensions of Local Rings
5G. Global Dimensions ofCommutative Noetherian Rings
Exercises for 5

3 More Theory of Modules
4 Rings of Quotients
5 More Rings of Quotients
6 Frobenius and Quasi-Frobenius Rings
7 Matrix Rings， Categories of Modules， and Morita Theory
References
Name Index
Subject Index

前言/序言

模與環講義 [Lectures on Modules and Rings] 下載 mobi epub pdf txt 電子書 格式

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