👉 Ring mathematics is a branch of abstract algebra that studies algebraic structures known as rings, which generalize the properties of integers and polynomials. A ring is a set equipped with two binary operations, typically addition and multiplication, that satisfy specific axioms: the set is an abelian group under addition, multiplication is associative, and multiplication distributes over addition. Rings can be commutative or non-commutative, and they may or may not have a multiplicative identity. Subrings are subsets of rings that themselves form rings under the same operations, and ideals are special subsets that help in constructing quotient rings. Ring homomorphisms are structure-preserving maps between rings, and they play a crucial role in understanding the relationships between different rings. This field is foundational in number theory, algebraic geometry, and computer science, particularly in areas like cryptography and coding theory.
