Algebraic properties of special rings of formal series

The \(K\)-algebra \(K_{S}[[X]]\) of Newton interpolating series is constructed by means of Newton interpolating polynomials with coefficients 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 \(K_{S}[[X]]\) 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].