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Some Properties of First Order Differential Operators
Département de Mathématiques, Faculté des Sciences et Techniques, Université Marien Ngouabi, Brazzaville, Congo
- 1 Département de Mathématiques, Faculté des Sciences et Techniques, Université Marien Ngouabi, Brazzaville, Congo
Advances in Pure Mathematics·Volume 09 (2019)·Pages 934–943·Published 4 November 2019·DOI10.4236/apm.2019.911046
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Abstract
We study some properties of first order differential operators from an algebraic viewpoint. We show this last can be decomposed in sum of an element of a module and a derivation. From a geometric viewpoint, we give some properties on the algebra of smooth functions. The Dirac mass at a point is the best example of first order differential operators at this point. This allows to construct a basis of this set and its dual basis.
KeywordsCommutative AlgebraDifferential OperatorsModule of Differentials
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