AUTHORS: Michael Gr. Voskoglou
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Properties are studied in this work of a differential ring R, its ideals and the ideals of iterated skew polynomial rings over R defined with respect to a finite set of commuting derivations of R. In particular, it is shown that, if P is a prime d-ideal of a commutative ring R for some derivation d of R, then the ring d-1(P) is integrally closed in R, while if R is a local ring and its maximal ideal M is not invariant under d, then M2 +d(M2 ) = M. Also the concept of the integration of R associated to a given derivation of R is introduced, the conditions under which this integration becomes a derivation of R are obtained and some consequences are derived in the form of two corollaries. The new concept of integration of R generalizes basic features of the indefinite integrals.
KEYWORDS: - Derivations, Integrations associated to derivations, Differential ideals, Iterated skew polynomial rings (ISPRs).
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