On Differentiability and Integrability of Rings

S. R. Gaikwad, A R Gotmare

Abstract: In this paper we study properties of the differential ideals of a ring R and of the iterated skew polynomial rings over R defined with respect to a finite set of commuting derivations of R. The concept of the integration of R associated to a given derivation of R is also introduced and some fundamental properties are studied. This new concept generalizes basic features of the indefinite integrals.

Keywords: Derivations and integrations associated to derivations