Non-holonomic Ideals in the Plane and Absolute Factoring

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dc.creatorGrigoriev, D.
dc.creatorSchwarz, F.
dc.date2008-11-09
dc.date.accessioned2026-07-07T10:17:09Z
dc.date.available2026-07-07T10:17:09Z
dc.descriptionWe study {\it non-holonomic} overideals of a left differential ideal $J\subset F[\partial_x, \partial_y]$ 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.
dc.identifierhttps://arxiv.org/abs/0811.1368
dc.identifierhttp://arxiv.org/abs/0811.1368
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173758
dc.subjectAnalysis of PDEs
dc.subjectRings and Algebras
dc.subject35A25, 35C05, 35G05
dc.titleNon-holonomic Ideals in the Plane and Absolute Factoring
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