invariant ring

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• Invariant theory — is a branch of abstract algebra that studies actions of groups on algebraic varieties from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit description of polynomial functions that do not …   Wikipedia

• Invariant basis number — In mathematics, the invariant basis number (IBN) property of a ring R is the property that all free modules over R are similarly well behaved as vector spaces, with respect to the uniqueness of their ranks. Definition A ring R has invariant basis …   Wikipedia

• Ring theory — In abstract algebra, ring theory is the study of rings algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their… …   Wikipedia

• Glossary of ring theory — Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. Contents 1 Definition of a ring 2 Types of… …   Wikipedia

• Gromov–Witten invariant — In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic… …   Wikipedia

• J-invariant — nome q on the unit diskIn mathematics, Klein s j invariant, regarded as a function of a complex variable tau;, is a modular function defined on the upper half plane of complex numbers. We can express it in terms of Jacobi s theta functions, in… …   Wikipedia

• Scale-invariant feature transform — Feature detection Output of a typical corner detection algorithm …   Wikipedia

• Geometric invariant theory — In mathematics Geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces. It was developed by David Mumford in 1965, using ideas from the paper… …   Wikipedia

• Hopf invariant — In mathematics, in particular in algebraic topology, the Hopf invariant is a homotopy invariant of certain maps between spheres. toc Motivation In 1931 Heinz Hopf used Clifford parallels to construct the Hopf map etacolon S^3 o S^2, and proved… …   Wikipedia

• Modular invariant of a group — In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic (usually dividing the order of the group). The study of modular invariants was originated in about 1914 by… …   Wikipedia

• Pluricanonical ring — In mathematics, the pluricanonical ring of an algebraic variety V (which is non singular), or of a complex manifold, is the graded ring R(V,K)=R(V,K V) of sections of powers of the canonical bundle K .Its n th graded component (for ngeq 0) is::R… …   Wikipedia