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Ext In English
Ext, ext or EXT may refer to: * Ext functor, used in the mathematical field of homological algebra * Ext (JavaScript library), a programming library used to build interactive web applications * Exeter Airport (IATA airport code), in Devon, England * Exeter St Thomas railway station (station code), in Exeter, England * Extended file system, a file system created for Linux * Exton station (Pennsylvania) (Amtrak station code), in Exton, Pennsylvania * Extremaduran language (ISO language code), spoken in Spain * Extremeroller, a former roller coaster at Worlds of Fun, Kansas City, Missouri * Cadillac Escalade EXT, a sport utility truck {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Ext Functor
In mathematics, the Ext functors are the derived functors of the Hom functor. Along with the Tor functor, Ext is one of the core concepts of homological algebra, in which ideas from algebraic topology are used to define invariants of algebraic structures. The group cohomology, cohomology of groups, Lie algebra cohomology, Lie algebras, and Hochschild cohomology, associative algebras can all be defined in terms of Ext. The name comes from the fact that the first Ext group Ext1 classifies group extension, extensions of one module (mathematics), module by another. In the special case of abelian groups, Ext was introduced by Reinhold Baer (1934). It was named by Samuel Eilenberg and Saunders MacLane (1942), and applied to topology (the universal coefficient theorem for cohomology). For modules over any ring (mathematics), ring, Ext was defined by Henri Cartan and Eilenberg in their 1956 book ''Homological Algebra''. Definition Let R be a ring and let R\text be the category (mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
