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Titlebook: Homology; Saunders Mac Lane Book 1995 Springer-Verlag Berlin Heidelberg 1995 Abelian group.Factor.algebra.auditor.cohomology.collaboration

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书目名称Homology
编辑Saunders Mac Lane
视频video
丛书名称Classics in Mathematics
图书封面Titlebook: Homology;  Saunders Mac Lane Book 1995 Springer-Verlag Berlin Heidelberg 1995 Abelian group.Factor.algebra.auditor.cohomology.collaboration
描述In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL­ LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug­ gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED­ RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE­ TER PUPPE,
出版日期Book 1995
关键词Abelian group; Factor; algebra; auditor; cohomology; collaboration; commutative ring; development; group; hom
版次1
doihttps://doi.org/10.1007/978-3-642-62029-4
isbn_softcover978-3-540-58662-3
isbn_ebook978-3-642-62029-4Series ISSN 1431-0821 Series E-ISSN 2512-5257
issn_series 1431-0821
copyrightSpringer-Verlag Berlin Heidelberg 1995
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Book 1995ogical algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL­ LING. A further development of homological ideas, with a view to their topological applications, came in
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1431-0821 des. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL­ LING. A further development of homological ideas, with a view to their topological application
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Homology of Complexes,elian group with a boundary operator is called a “differential group” or, when provided with dimensions, a “chain complex”. This chapter considers the algebraic process of constructing homology and cohomology groups from chain complexes. Basic is the fact (§ 4) that a short exact sequence of complex
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Extensions and Resolutions,sions, suitably classified by a congruence relation, are the elements of a group Ext.(.). To calculate this group, we present . as the quotient .=./. of a free module .; this process can be iterated as .=./., .=./.,… to give an exact sequence⋯→.→.→⋯→.→.→.→0called a “free resolution” of .. The comple
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Spectral Sequences,se successive approximations are codified in the notion of a spectral sequence. In this chapter we first formulate the mechanism of these sequences and then proceed to several applications, ending with another general theorem (the comparison theorem). Other applications will appear in the next chapt
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