The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the properties and specific features of the differential-geometrical structures. The using of skew-symmetric differential forms enables one to reveal a mechanism...

Fields of characteristic zero with several commuting derivations can be treated as fields equipped with a space of derivations that is closed under the Lie bracket. The existentially closed instances of such structures can then be given a coordinate-free characterization in terms of differential forms. The main tool for doing this is a generalization of the Frobenius Theorem of differential geo...

There is a fundamental asymmetry between algebras and their dual objects, coalgebras, namely that the dual of a coalgebra is an algebra, but the converse is only true in finite dimensions. We prove that there exists a differential graded coalgebra whose continuous dual is the differential graded algebra of differential forms. This coalgebra will be constructed as an explicit subspace of de Rham...

In this paper, we propose algorithms to compute differential Chow forms for prime differential ideals which are given by their characteristic sets. The main algorithm is based on an optimal bound for the order of a prime differential ideal in terms of its characteristic set under an arbitrary ranking, which shows the Jacobi bound conjecture holds in this case. Apart from the order bound, we als...

Differential forms are interesting and important generalizations of real functions and distributions. Many interesting results and applications of differential forms have recently been found in some fields, such as tensor analysis, potential theory, partial differential equations and quasiregular mappings, see [B], [C], [D1], [HKM], [I], [IL] and [IM]. In many cases, we need to know the integra...