oalogo2  

AUTHOR(S): 

Michael Gr. Voskoglou

 

TITLE

A Study on Smooth Varieties with Differentially Simple Coordinate Rings

pdf PDF

KEYWORDS

Derivations, Differentially simple rings, Algebraic sets, Singularities, Coordinate rings of smooth varieties

ABSTRACT

The notion of the algebraic sets was proved to be fundamental for the development of the Algebraic Geometry. In the paper at hands we study irreducible algebraic sets (varieties) with differentially simple coordinate rings. Starting from the fact that the coordinate ring of a singular variety does not admit simple derivations, we turn our attention to smooth varieties proving that the coordinate rings of the circle of the cylinder and of the real torus are differentially simple rings. However, this is not true for the coordinate rings of all smooth varieties; for example the coordinate ring of the real sphere does not admit simple derivations.

Cite this paper

Michael Gr. Voskoglou. (2017) A Study on Smooth Varieties with Differentially Simple Coordinate Rings. International Journal of Mathematical and Computational Methods, 2, 53-59