ALGEBRAIC PROPERTIES OF SPECIAL RINGS OF FORMAL SERIES

The K-algebra KS]]X[[of Newton interpolating series is constructed by means of Newton interpolating polynomials with coeffcients in an arbitrary field K (see Section 1) and a sequence S of elements K. In this paper we prove that this algebra is an integral domain if and only if S is a constant sequence. If K is a non-archimedean valued field we obtain that a K-subalgebra of convergent series of KS]]X[[is isomorphic to Tate algebra )see Theorem 3 (in one variable and by using this representation we obtain a general proof of a theorem of Strassman (see Corollary 1.(In the case of many variables other results can be found in ]2. [