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A fundamental algebraic structure known as a ring is used extensively in abstract algebra. It comprises a set equipped with two binary operations that generalize arithmetic's addition and multiplication. Theorems from arithmetic are thereby extended to objects like polynomials, series, matrices, and functions. An abelian group with an associative second binary operation, distributive over the abelian group operation, and possessing an identity element is what makes up a ring. Borrowing concepts from integers, this abelian group operation is known as addition, while the second binary operation is termed multiplication. Commutative or noncommutative (meaning the order of two elements multiplied has no effect) greatly impacts the behavior of rings as abstract entities. Consequently, commutative algebra is a primary concern in ring theory, with its development significantly influenced by problems and ideas naturally arising from algebraic number theory and geometry. The integers under addition and multiplication form examples of commutative rings, along with polynomial sets and coordinate rings of affine varieties. Group rings and operator algebras represent noncommutative instances. Key players include Dedekind, Hilbert, Fraenkel, and Noether in shaping the understanding of rings.