翻訳と辞書 Words near each other ・ Homopolar generator ・ Homopolar motor ・ Homopolysaccharide ・ Homoptera ・ Homopterus ・ Homopus ・ Homopus areolatus ・ Homopus boulengeri ・ Homopus femoralis ・ Homopus signatus ・ Homopus solus ・ Homoquinolinic acid ・ Homologation (motorsport) ・ Homologation reaction ・ HomoloGene ・ Homological algebra ・ Homological conjectures in commutative algebra ・ Homological dimension ・ Homological integration ・ Homological mirror symmetry ・ Homologous chromosome ・ Homologous desensitization ・ Homologous recombination ・ Homologous series ・ Homologous temperature ・ Homology ・ Homology (anthropology) ・ Homology (biology) ・ Homology (chemistry) ・ Homology (mathematics) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Homological algebra ： ウィキペディア英語版 Homological algebra Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies) at the end of the 19th century, chiefly by Henri Poincaré and David Hilbert. The development of homological algebra was closely intertwined with the emergence of category theory. By and large, homological algebra is the study of homological functors and the intricate algebraic structures that they entail. One quite useful and ubiquitous concept in mathematics is that of chain complexes, which can be studied both through their homology and cohomology. Homological algebra affords the means to extract information contained in these complexes and present it in the form of homological invariants of rings, modules, topological spaces, and other 'tangible' mathematical objects. A powerful tool for doing this is provided by spectral sequences. From its very origins, homological algebra has played an enormous role in algebraic topology. Its sphere of influence has gradually expanded and presently includes commutative algebra, algebraic geometry, algebraic number theory, representation theory, mathematical physics, operator algebras, complex analysis, and the theory of partial differential equations. K-theory is an independent discipline which draws upon methods of homological algebra, as does the noncommutative geometry of Alain Connes. ==History of homological algebra== Homological algebra began to be studied in its most basic form in the 1800s as a branch of topology, but it wasn't until the 1940s that it became an independent subject with the study of objects such as the ext functor and the tor functor, among others.〔History of Homological Algebra, by Chuck Weibel, pp.797-836 in the book The History of Topology, ed. I.M. James, Elsevier, 1999〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Homological algebra」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.