crusade 发表于 2025-3-21 18:10:23
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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修正案 发表于 2025-3-22 07:20:35
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哪有黄油 发表于 2025-3-22 09:24:00
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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 complexHay-Fever 发表于 2025-3-22 19:29:02
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 compleAntimicrobial 发表于 2025-3-23 00:48:00
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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