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In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms of linear maps. The module construction is analogous to the construction of the tensor product of vector spaces, but can be carried out for a pair of modules over a commutative ring resulting ...
Group cohomology. In mathematics (more specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G -module M to elucidate ...
edu.gcfglobal.org. edu.GCFGlobal.org (formerly GCFLearnFree.org) is a free online educational website focusing on technology, job training, reading, and math skills. The site is a program of the Goodwill Community Foundation Inc. (GCF). All content in English is created in Raleigh, North Carolina and all the content in Spanish Bogotá, Colombia ...
Free module. In mathematics, a free module is a module that has a basis, that is, a generating set consisting of linearly independent elements. Every vector space is a free module, [1] but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules.
for all a 1 and a 2 in M and all g in G, where g·a denotes ρ(g,a). A right G-module is defined similarly. Given a left G-module M, it can be turned into a right G-module by defining a·g = g −1 ·a. A function f : M → N is called a morphism of G-modules (or a G-linear map, or a G-homomorphism) if f is both a group homomorphism and G ...
The testing effect (also known as retrieval practice, active recall, practice testing, or test-enhanced learning) [1][2][3] suggests long-term memory is increased when part of the learning period is devoted to retrieving information from memory. [4] It is different from the more general practice effect, defined in the APA Dictionary of ...
Resolution (algebra) In mathematics, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution[1]) is an exact sequence of modules (or, more generally, of objects of an abelian category) that is used to define invariants characterizing the structure of a specific module or object ...
The Graduate Aptitude Test in Engineering (GATE) is an entrance examination conducted in India that tests the undergraduate subjects of engineering and sciences for admission to technical postgraduate programs. GATE is conducted jointly by the Indian Institute of Science and seven Indian Institutes of Technologies at Roorkee, Delhi, Guwahati ...
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