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An elementary approach to homological algebra

An elementary approach to homological algebra

자료유형
단행본
개인저자
Vermani, L. R. (Lekh R.)
서명 / 저자사항
An elementary approach to homological algebra / L.R. Vermani.
발행사항
Boca Raton :   Chapman & Hall/CRC,   2003.  
형태사항
315 p. : ill. ; 24 cm.
총서사항
Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ;130
ISBN
1584884002 (alk. paper)
서지주기
Includes bibliographical references (p. [309]-312) and index.
일반주제명
Algebra, Homological.
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008 110119s2003 flua b 001 0 eng d
010 ▼a 2003046075
020 ▼a 1584884002 (alk. paper)
040 ▼a DLC ▼c DLC ▼d DLC ▼d 211009
050 0 0 ▼a QA169 ▼b .V48 2003
082 0 0 ▼a 512/.55 ▼2 22
084 ▼a 512.55 ▼2 DDCK
090 ▼a 512.55 ▼b V522e
100 1 ▼a Vermani, L. R. ▼q (Lekh R.)
245 1 3 ▼a An elementary approach to homological algebra / ▼c L.R. Vermani.
260 ▼a Boca Raton : ▼b Chapman & Hall/CRC, ▼c 2003.
300 ▼a 315 p. : ▼b ill. ; ▼c 24 cm.
490 1 ▼a Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; ▼v 130
504 ▼a Includes bibliographical references (p. [309]-312) and index.
650 0 ▼a Algebra, Homological.
830 0 ▼a Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; ▼v 130.
945 ▼a KLPA

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컨텐츠정보

목차

MODULES
Modules
Free Modules
Exact Sequences
Homomorphisms
Tensor Product of Modules
Direct and Inverse Limits
Pull Back and Push Out
CATEGORIES AND FUNCTORS
Categories
Functors
The Functors Hom and Tensor
PROJECTIVE AND INJECTIVE MODULES
Projective Modules
Injective Modules
Baer's Criterion
An Embedding Theorem
HOMOLOGY OF COMPLEXES
Ker-Coker Sequence
Connecting Homomorphism: The General Case
Homotopy
DERIVED FUNCTORS
Projective Resolutions
Injective Resolutions
Derived Functors
TORSION AND EXTENSION FUNCTORS
Derived Functors--Revisited
Torsion and Extension Functors
Some Further Properties of Torsion Functors
Tor and Direct Limits
THE FUNCTOR ExtnR
Ext1 and Extensions
Baer Sum of Extensions
Some Further Properties of Extension Functors
HEREDITARY AND SEMIHEREDITARY RINGS
Hereditary Rings and Dedekind Domains
Invertible Ideals and Dedekind Rings
Semihereditary and Prufer Rings
UNIVERSAL COEFFICIENT THEOREM
Universal Coefficient Theorem for Homology
Universal Coefficient Theorem for Cohomology
The Kunneth Formula: A Special Case
DIMENSIONS OF MODULES AND RINGS
Projectively and Injectively Equivalent Modules
Dimensions of Modules and Rings
Global Dimension of Rings
Global Dimension of Noetherian Rings
Global Dimension of Artin Rings
COHOMOLOGY OF GROUPS
Homology and Cohomology Groups
Some Examples
The Groups H0(G,A) and H0(G,A)
The Groups H1(G,A) and H1(G,A)
Homology and Cohomology of Direct Sums
The Bar Resolution
Second Cohomology Group and Extensions
Some Homomorphisms
Some Exact Sequences
SOME APPLICATIONS
An Exact Sequence
Outer Automorphisms of p-Groups
A Theorem of Magnus
BIBLIOGRAPHY
INDEX


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