Commutative algebra is a branch of abstract algebra that studies commutative rings and their properties. It deals with structures like ideals, modules, and homomorphisms in the context of commutative rings, which are rings where multiplication is commutative. One of the main goals of commutative algebra is to understand the structure and behavior of algebraic objects like polynomial rings, power series rings, and algebraic varieties. This area of mathematics has applications in various fields like algebraic geometry, number theory, and cryptography. Key topics in commutative algebra include prime ideals, localization, integral extensions, Noetherian rings, and unique factorization. Researchers in this field also study algebraic techniques to solve problems related to geometry, algebraic number theory, and coding theory.