Non-holonomic overideals of differential ideals in two variables and absolute factoring
نویسنده
چکیده
We study non-holonomic overideals of a (left) differential ideal J ⊂ F [dx, dy ] 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 symbol symb(P ) (being 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. AMS Subject Classifications: 35A25, 35C05, 35G05
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