✦ LIBER ✦

The Differential Ideal [ P ] : M∞

✍ Scribed by Sally Morrison

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 442 KB
Volume: 28
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.1999.0318

No coin nor oath required. For personal study only.

✦ Synopsis

Let F be a finite subset of the differential polynomial algebra k{y 1 , . . . , yn}. In order to determine membership in the radical differential ideal {F }, one is led to express {F } as the intersection of differential ideals of the form [P ] : M ∞ for suitable subsets P and M of k{y 1 , . . . , yn}. One criterion for "suitability" is that the ideal [P ] : M ∞ should be radical; another is that the question of membership in this ideal should be reducible to the question of membership in its algebraic counterpart (P ) : M ∞ . Lazard's lemma provides sufficient conditions for the first criterion to hold; Rosenfeld's lemma provides sufficient conditions for the second criterion to hold. In this paper, we prove substantially strengthened versions of both of these results, and apply them to Mansfield's algorithms (Mansfield, 1993) for solving systems of PDEs.

📜 SIMILAR VOLUMES

The Ideals of Free Differential Algebras

✍ C Frønsdal; A Galindo 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 243 KB

We consider the free C-algebra B B with N generators , together relationship to generalized, quantized Kac᎐Moody algebras suggests an approach to the problem of classification of these algebras.

M-Ideals and the "Basic Inequality"

✍ D. Werner 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 397 KB

Two methods which can be used to show that, on a Banach space \(X\), every bounded linear operator has a best compact approximation, namely the basic inequality method and the method of \(M\)-ideals, are shown to be basically equivalent. Thus, the paper responds to a question posed by S. Axler, I. D

Ideals in Polynomial Rings and the Modul

Ideals in Polynomial Rings and the Module of Differentials

✍ Satya Mandal 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 65 KB

Remarks on M-Ideals of Compact Operators

Remarks on M-Ideals of Compact Operators on X ⊕p X

✍ Eve Oja; Dirk Werner 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 473 KB

We characterize those BANACH spaces X for which K(X 0, X) is an M-ideal in L(X 0, X) by means of a variant of the compact metric approximation property. As a consequence we obtain that such a space X must be hereditarily P-rich.

The Ideal Detector

✍ Keith Birkinshaw; David P. Langstaff 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 394 KB

Focal plane detectors (FPDs) offer a very large increase in collection efficiency of ions compared with the traditional single-slit detector. Several types of F'PD are in existence. The integration of a complete high resolution discrete detector FPD system including computer interface on a silicon c

The Ideal Cut

✍ Elinor Gray 📂 Fiction 📅 2013 🏛 Goodreads M/M Romance Group 🌐 English ⚖ 31 KB 👁 1 views

Clayton Gaumont, alias The Ghost, is one of the most skilled, least known diamond thieves in the world, and tonight is just another night on the job. The party is in full swing, the guests are all occupied, and a ten million dollar prize sits unguarded just over their heads. But bumping into sexy, m