Ring Theory

Ring theory is a branch of abstract algebra that studies the structure and properties of rings, which are algebraic structures consisting of a set equipped with two binary operations satisfying certain axioms. The main focus of ring theory is to investigate the properties of these structures, such as the existence of units, zero divisors, and ideals, as well as the relationships between different types of rings, such as commutative and non-commutative rings. Key concepts in ring theory include ring homomorphisms, ring ideals, and the classification of rings based on properties such as integrality, divisibility, and factorization.