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Basic homological algebra

Basic homological algebra (3회 대출)

자료유형
단행본
개인저자
Osborne, M. Scott.
서명 / 저자사항
Basic homological algebra / M. Scott Osborne.
발행사항
New York :   Springer,   2000.  
형태사항
x 395 p. : ill. ; 25 cm.
총서사항
Graduate texts in mathematics ; 196
ISBN
038798934X (hc. : alk. paper)
서지주기
Includes bibliographical references (p. [383]-387) and index.
일반주제명
Algebra, Homological.
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010 ▼a 99046582
020 ▼a 038798934X (hc. : alk. paper)
040 ▼a DLC ▼c DLC ▼d DLC ▼d 244002
042 ▼a pcc
049 0 ▼l 151095951
050 0 0 ▼a QA169 ▼b .O83 2000
082 0 0 ▼a 512/.55 ▼2 21
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100 1 ▼a Osborne, M. Scott.
245 1 0 ▼a Basic homological algebra / ▼c M. Scott Osborne.
260 ▼a New York : ▼b Springer, ▼c 2000.
300 ▼a x 395 p. : ▼b ill. ; ▼c 25 cm.
440 0 ▼a Graduate texts in mathematics ; ▼v 196
504 ▼a Includes bibliographical references (p. [383]-387) and index.
650 0 ▼a Algebra, Homological.

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 세종학술정보원/과학기술실/ 청구기호 512.55 O81b 등록번호 151095951 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

목차

1 Categories.- 2 Modules.- 2.1 Generalities.- 2.2 Tensor Products.- 2.3 Exactness of Functors.- 2.4 Projectives, Injectives, and Flats.- 3 Ext and Tor.- 3.1 Complexes and Projective Resolutions.- 3.2 Long Exact Sequences.- 3.3 Flat Resolutions and Injective Resolutions.- 3.4 Consequences.- 4 Dimension Theory.- 4.1 Dimension Shifting.- 4.2 When Flats are Projective.- 4.3 Dimension Zero.- 4.4 An Example.- 5 Change of Rings.- 5.1 Computational Considerations.- 5.2 Matrix Rings.- 5.3 Polynomials.- 5.4 Quotients and Localization.- 6 Derived Functors.- 6.1 Additive Functors.- 6.2 Derived Functors.- 6.3 Long Exact Sequences-I. Existence.- 6.4 Long Exact Sequences-II. Naturality.- 6.5 Long Exact Sequences-III. Weirdness.- 6.6 Universality of Ext.- 7 Abstract Homologieal Algebra.- 7.1 Living Without Elements.- 7.2 Additive Categories.- 7.3 Kernels and Cokernels.- 7.4 Cheating with Projectives.- 7.5 (Interlude) Arrow Categories.- 7.6 Homology in Abelian Categories.- 7.7 Long Exact Sequences.- 7.8 An Alternative for Unbalanced Categories.- 8 Colimits and Tor.- 8.1 Limits and Colimits.- 8.2 Adjoint Functors.- 8.3 Directed Colimits, ?, and Tor.- 8.4 Lazard's Theorem.- 8.5 Weak Dimension Revisited.- 9 Odds and Ends.- 9.1 Injective Envelopes.- 9.2 Universal Coefficients.- 9.3 The Kunneth Theorems.- 9.4 Do Connecting Homomorphisms Commute?.- 9.5 The Ext Product.- 9.6 The Jacobson Radical, Nakayama's Lemma, and Quasilocal Rings.- 9.7 Local Rings and Localization Revisited (Expository).- A GCDs, LCMs, PIDs, and UFDs.- B The Ring of Entire Functions.- C The Mitchell-Freyd Theorem and Cheating in Abelian Categories.- D Noether Correspondences in Abelian Categories.- Solution Outlines.- References.- Symbol Index.


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