Local ring

A local ring is a special type of mathematical structure used in algebra that focuses on a particular point or "local" area within a larger system. It contains elements that represent functions or quantities near that point, and has a unique maximal ideal, meaning there's a biggest subset of elements that behave like "small" or "negligible" parts. This setup helps mathematicians study local properties of shapes or spaces, such as their behavior near a specific point, by simplifying the complex global structure to a more manageable local context.