STABLE ELEMENTS OF BANACH AND FRECHET ALGEBRAS

We introduce an algebraic notion-stability-for an element of a commuta tive ring. It is shown that the stable elements of Banach algebras, an d of Frechet algebras, may be simply described. Part of the theory of power-series embeddings, given in [1] and [4], is seen to be of a pure ly algebraic nature. This approach leads to other natural questions.