Abelian von Neumann algebra

Abelian von Neumann algebras are sets of mathematical objects that can have different types of mathematical operations performed on them. This might sound confusing, but think of it like a machine that can do different kinds of calculations. It can do additions, subtractions, multiplications, and divisions when the right parts are put in and the right buttons are pushed. The machine is the Abelian von Neumann algebra, and the parts and buttons are the mathematical operations.