Module Theory

Module theory is a branch of mathematics that generalizes vector spaces, but instead of using fields (like real or complex numbers), it uses rings, which can be more complex algebraic structures. A module is a mathematical object where elements can be scaled and added, following rules similar to vector spaces, but with scalars from a ring. This framework helps mathematicians study algebraic systems, like symmetry structures or solutions to equations, in a more flexible way, extending the concepts of linear algebra to broader contexts where the underlying scalars don’t necessarily form a field.