commutative square

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• Commutative diagram — For help on drawing commutative diagrams on Wikipedia, see meta:Help:Displaying a formula#Commutative diagrams. In mathematics, and especially in category theory, a commutative diagram is a diagram of objects (also known as vertices) and… …   Wikipedia

• Combinatorial commutative algebra — is a relatively new, rapidly developing mathematical discipline. As the name implies, it lies at the intersection of two more established fields, commutative algebra and combinatorics, and frequently uses methods of one to address problems… …   Wikipedia

• Homological conjectures in commutative algebra — In mathematics, the homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of interrelated (sometimes surprisingly so) conjectures relating various homological properties …   Wikipedia

• Euler's four-square identity — In mathematics, Euler s four square identity says that the product of two numbers, each of which being a sum of four squares, is itself a sum of four squares. Specifically::(a 1^2+a 2^2+a 3^2+a 4^2)(b 1^2+b 2^2+b 3^2+b 4^2)=,::(a 1 b 1 a 2 b 2 a… …   Wikipedia

• Split-complex number — A portion of the split complex number plane showing subsets with modulus zero (red), one (blue), and minus one (green). In abstract algebra, the split complex numbers (or hyperbolic numbers) are a two dimensional commutative algebra over the real …   Wikipedia

• Cotangent complex — In mathematics the cotangent complex is a roughly a universal linearization of a morphism of geometric or algebraic objects. Cotangent complexes were originally defined in special cases by a number of authors. Luc Illusie, Daniel Quillen, and M.… …   Wikipedia

• Triangulated category — A triangulated category is a mathematical category satisfying some axioms that are based on the properties of the homotopy category of spectra, and the derived category of an abelian category. A t category is a triangulated category with a t… …   Wikipedia

• Limit (category theory) — In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products and inverse limits. The dual notion of a colimit generalizes constructions such as disjoint… …   Wikipedia

• Коммутативная диаграмма — В математике (особенно в теории категорий), коммутативная диаграмма изображаемая в наглядном виде структура наподобие графа, вершинами которой служат объекты определённой категории, а рёбрами морфизмы. Коммутативность означает, что для любых… …   Википедия

• Determinant — This article is about determinants in mathematics. For determinants in epidemiology, see Risk factor. In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific… …   Wikipedia

• Cayley–Hamilton theorem — In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Hamilton) states that every square matrix over the real or complex field satisfies its own characteristic equation.More precisely; if A is… …   Wikipedia