On the existence of elements of non-nilpotent finite closed descent in commutative radical Frechet algebras

It is established that in a commutative radical Frechet algebra, elements of non-nilpotent finite closed descent exist if a locally non-nilpotent element of locally finite closed descent exists. Thus if C[[X]] can be embedded into the unitization of the algebra in such a way that X is mapped to an element which is locally non-nilpotent, then it is possible to embed the 'structurally rich' algebra C-w1.