graded algebra

An algebraPlanetmathPlanetmath A over a graded ringMathworldPlanetmath B is graded if it is itself a graded ring and a graded moduleMathworldPlanetmath over B such that


where Ai, i, are submodules of A. More generally, one can replace by a monoid or semigroup G. In which case, A is called a G-graded algebraMathworldPlanetmath. A graded algebra then is the same thing as an -graded algebra.

Examples of graded algebras include the polynomial ring k[X] being an -graded k-algebra, and the exterior algebra.

Title graded algebra
Canonical name GradedAlgebra
Date of creation 2013-03-22 12:45:47
Last modified on 2013-03-22 12:45:47
Owner mhale (572)
Last modified by mhale (572)
Numerical id 8
Author mhale (572)
Entry type Definition
Classification msc 16W50
Related topic GradedModule
Related topic SuperAlgebra
Related topic LieSuperalgebra
Related topic LieSuperalgebra3