T-ideal
Let R be a commutative ring and R⟨X⟩ be a free algebra over R on a set X of non-commuting variables. A two-sided ideal
I of R⟨X⟩ is called a T-ideal if ϕ(I)⊆I for any R-endomorphism
ϕ of R⟨X⟩.
For example, let A be a R-algebra. Define 𝒯(A) to be the set of all polynomial identities (http://planetmath.org/PolynomialIdentityAlgebra) f∈R⟨X⟩ for A. Then 𝒯(A) is a T-ideal of R⟨X⟩. 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 |