TITLE:
Some Properties of First Order Differential Operators
AUTHORS:
Servais Cyr Gatse
KEYWORDS:
Commutative Algebra, Differential Operators, Module of Differentials
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.9 No.11,
November
27,
2019
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.