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residue algebra

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  • Residue field — In mathematics, the residue field is a basic construction in commutative algebra. If R is a commutative ring and m is a maximal ideal, then the residue field is the quotient ring k = R / m , which is a field. Frequently, R is a local ring and m… …   Wikipedia

  • Koszul algebra — In abstract algebra, a Koszul algebra R is a graded k algebra over which the residue field k has a linear minimal graded free resolution, i.e. , there exists an exact sequence: :cdots ightarrow R( i)^{b i} ightarrow cdots ightarrow R( 2)^{b 2}… …   Wikipedia

  • Quadratic residue — In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract… …   Wikipedia

  • Valuation (algebra) — In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field. They generalize to commutative algebra the notion of size… …   Wikipedia

  • Hecke algebra — is the common name of several related types of associative rings in algebra and representation theory. The most familiar of these is the Hecke algebra of a Coxeter group , also known as Iwahori Hecke algebra, which is a one parameter deformation… …   Wikipedia

  • Frobenius algebra — In mathematics, especially in the fields of representation theory and module theory, a Frobenius algebra is a finite dimensional unital associative algebra with a special kind of bilinear form which gives the algebras particularly nice duality… …   Wikipedia

  • Norm residue isomorphism theorem — In the mathematical field of algebraic K theory, the norm residue isomorphism theorem is a long sought result whose complete proof was announced in 2009. It previously was known as the Bloch–Kato conjecture, after Spencer Bloch and Kazuya Kato,… …   Wikipedia

  • Noncommutative residue — In mathematics, noncommutative residue, defined independently by M. Wodzicki (1984) and Guillemin (1985), is a certain trace on the algebra of pseudodifferential operators on a compact differentiable manifold that is expressed via a local density …   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

  • List of mathematics articles (R) — NOTOC R R. A. Fisher Lectureship Rabdology Rabin automaton Rabin signature algorithm Rabinovich Fabrikant equations Rabinowitsch trick Racah polynomials Racah W coefficient Racetrack (game) Racks and quandles Radar chart Rademacher complexity… …   Wikipedia

  • Modular arithmetic — In mathematics, modular arithmetic (sometimes called clock arithmetic) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value the modulus. The Swiss mathematician Leonhard Euler pioneered the modern… …   Wikipedia

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