Commutative Algebra is a branch of mathematics that studies commutative rings, which are algebraic structures where the multiplication operation is commutative. This means that the order in which two elements are multiplied does not affect the result. Commutative algebra provides the foundation for various areas in mathematics, including algebraic geometry and number theory. One of the key concepts in commutative algebra is the idea of an ideal, which is a special subset of a ring that allows for the construction of quotient rings. These ideals help mathematicians understand the structure of rings and their properties. The study of modules over rings is also an important aspect, as it generalizes the notion of vector spaces.