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Non-holonomic Ideals in the Plane and Absolute Factoring | | D.Grigoriev
; F.Schwarz
; | | Date: |
9 Nov 2008 | | Abstract: | We study {it non-holonomic} overideals of a left differential ideal
$Jsubset F[partial_x, partial_y]$ in two variables where $F$ is a
differentially closed field of characteristic zero. The main result states that
a principal ideal $J=< P>$ generated by an operator $P$ with a separable {it
symbol} $symb(P)$, which is a homogeneous polynomial in two variables, has a
finite number of maximal non-holonomic overideals. This statement is extended
to non-holonomic ideals $J$ with a separable symbol. As an application we show
that in case of a second-order operator $P$ the ideal $<P>$ has an infinite
number of maximal non-holonomic overideals iff $P$ is essentially ordinary. In
case of a third-order operator $P$ we give few sufficient conditions on $<P>$
to have a finite number of maximal non-holonomic overideals. | | Source: | arXiv, 0811.1368 | | Services: | Forum | Review | PDF | Favorites | |
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