Some Properties of First Order Differential Operators  

作　　者：Servais Cyr Gatse 

机构地区：[1]Département de Mathématiques, Faculté des Sciences et Techniques, Université Marien Ngouabi, Brazzaville, Congo

出　　处：《Advances in Pure Mathematics》2019年第11期934-943,共10页理论数学进展（英文）

摘　　要：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.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.

关 键 词：COMMUTATIVE ALGEBRA DIFFERENTIAL OPERATORS MODULE of DIFFERENTIALS 

分 类 号：O17[理学—数学]