D-module

A D-module is a mathematical framework used to study functions and their derivatives collectively through algebraic structures called differential operators. Think of it as a way to algebraically capture how functions change, enabling the analysis of complex systems in geometry, physics, and algebraic analysis. Instead of focusing on individual functions, D-modules organize their differential behaviors, allowing mathematicians to understand solutions to differential equations and their properties in a broad, unified way. This concept helps bridge algebra and geometry, providing powerful tools for understanding how mathematical objects behave under differentiation.