环论, or "ring theory," is a branch of abstract algebra that studies algebraic structures known as rings. A ring consists of a set equipped with two binary operations: addition and multiplication. These operations must satisfy certain properties, such as associativity and distributivity. Rings can be used to generalize concepts from arithmetic and are fundamental in various areas of mathematics. In ring theory, important concepts include ideals, homomorphisms, and fields. Ideals are special subsets of rings that allow for the construction of quotient rings, while homomorphisms are structure-preserving maps between rings. Fields, which are rings with additional properties, play a crucial role in many mathematical applications.