R-module

An R-module is a mathematical structure that generalizes the concept of vectors but works over a ring (a set with addition and multiplication) instead of just a field. Think of it like a space where you can add elements and scale them by elements from the ring, similar to how vectors can be scaled by numbers. This framework allows mathematicians to study complex algebraic systems in a unified way, encompassing familiar structures like vector spaces over fields and more intricate algebraic objects related to rings and modules.