Let R be a commutative ring and RX be a free algebraMathworldPlanetmath over R on a set X of non-commuting variables. A two-sided idealMathworldPlanetmath I of RX is called a T-ideal if ϕ(I)I for any R-endomorphismMathworldPlanetmathPlanetmath ϕ of RX.

For example, let A be a R-algebraMathworldPlanetmathPlanetmath. Define 𝒯(A) to be the set of all polynomial identities (http://planetmath.org/PolynomialIdentityAlgebra) fRX for A. Then 𝒯(A) is a T-ideal of RX. 𝒯(A) is called the T-ideal of of A.

Title T-ideal
Canonical name Tideal
Date of creation 2013-03-22 14:21:12
Last modified on 2013-03-22 14:21:12
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 7
Author CWoo (3771)
Entry type Definition
Classification msc 16R10