eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2019-02-09 7 2 75 78 10.12691/ajams-7-2-4 AJAMS2019724 article Michael Gr. Voskoglou mvosk@hol.gr 1 Department of Mathematical Sciences, Graduate T. E. I. of Western Greece, Patras, Greece In this paper properties are studied 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 funamental properties of it are studied. This new concept generalizes basic features of the indefinite integrals. http://pubs.sciepub.com/ajams/7/2/4/ajams-7-2-4.pdf derivations integrations associated to derivations differential ideals iterated skew polynomial rings (ISPRs)