WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 18, 2019
On Properties of Differential Rings
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Abstract: 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 M^2+d(M^2) = 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.
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Keywords: Derivations, Integrations associated to derivations, Differential ideals, Iterated skew polynomial rings (ISPRs)
Pages: 112-117
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 18, 2019, Art. #15