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Hilbert-type dimension polynomials of intermediate difference-differential field extensions
Alexander Levin
Let be an inversive difference-differential field and a (not necessarily inversive) finitely generated difference-differential field extension of . We consider the natur…
Dimension Polynomials and the Einstein's Strength of Some Systems of Quasi-linear Algebraic Difference Equations
Alexander Evgrafov, Alexander Levin
In this paper we present a method of characteristic sets for inversive difference polynomials and apply it to the analysis of systems of quasi-linear algebraic difference equations…
Bivariate Kolchin-type dimension polynomials of non-reflexive prime difference-differential ideals. The case of one translation
Alexander Levin
We use the method of characteristic sets with respect to two term orderings to prove the existence and obtain a method of computation of a bivariate Kolchin-type dimension polynomi…
Multivariate Difference-Differential Dimension Polynomials and New Invariants of Difference-Differential Field Extensions
Alexander Levin
In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method…
Multivariate Difference-Differential Dimension Polynomials
Alexander Levin
In this paper we generalize the Ritt-Kolchin method of characteristic sets and the classical Gröbner basis technique to prove the existence and obtain methods of computation of mul…
On the ascending chain condition for mixed difference ideals
Alexander Levin
We show that the ring of difference polynomials over a difference field does not satisfy the ascending chain condition for mixed difference ideals. This result solves an open probl…