The Construction of Noetherian Operators
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文摘
We give an elementary and constructive, purely algebraic proof for the existence of noetherian differential operators for primary submodules of finite-dimensional free modules over polynomial algebras. By means of these operators the submodule can be described by differential conditions on the associated characteristic variety. This important result and the terminology are due to V. P. Palamodov. However, his, L. Ehrenpreis' and later J.-E. Björk's proofs of the existence theorem use complicated algebraic and analytic techniques and are not constructive as far as we see. The idea to characterize primary ideals by their associated differential operators is due to W. Gröbner. But M. Noether's Fundamentalsatz is based on similar ideas and is obviously the origin of Palamodov's terminology.