Symmetric Derivations on Kahler Modules

TL;DR

This paper introduces generalized symmetric derivations on Kähler modules, exploring their properties and relationships with projective dimensions, leading to new insights in the structure of Kähler modules.

Contribution

It defines generalized symmetric derivations on Kähler modules and investigates their impact on projective dimensions, providing novel theoretical results.

Findings

Relationships between projective dimensions of mi^{(1)}(R/k) and mi^{(2)}(R/k)

New results connecting symmetric derivations with Kähler modules

Enhanced understanding of the structure of Kähler modules

Abstract

In this paper, we define generalized symmetric derivations on K\"{a}hler modules. We give the relationships between the projective dimensions of $\Omega^{(1)}(R/k)$ and $\Omega^{(2)}(R/k)$ by using the symmetric derivation.We then give some interesting results by using this definition and related to K\"{a}hler modules and symmetric derivations.