Update free_associative_algebra.md

Added some math facts.

docs/src/NoncommutativeAlgebra/free_associative_algebra.md

@@ -20,12 +20,16 @@ ideal(g::Vector{T}) where T <: FreeAssAlgElem
 
 ### Ideal Membership
 
+Non-commutative polynomial rings are not Noetherian.  Hence, in general, Groebner bases do not exist.  Hence calling the functions below may not terminate.  Picking suitable term orders is difficult in the noncommutative case.  Therefore, we fix the term order to be degree reverse lexicographic.
+
+Setting the parameter `deg_bound` to a positive value yields the truncation of the Groebner bases to a fixed degree.  Such a truncation is always finite.
+
 ```@docs
-ideal_membership(a::FreeAssAlgElem, I::FreeAssAlgIdeal, deg_bound::Int)
+groebner_basis(I::FreeAssAlgIdeal, deg_bound::Int=-1; protocol::Bool=false)
 ```
 
-The groebner basis computation used for `ideal_membership` is implemented in the function `groebner_basis`.
+If a finite Gröbner basis exists, it solves the ideal membership problem.
 
 ```@docs
-groebner_basis(I::FreeAssAlgIdeal, deg_bound::Int=-1; protocol::Bool=false)
+ideal_membership(a::FreeAssAlgElem, I::FreeAssAlgIdeal, deg_bound::Int)
 ```