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The term "ring" originates from Chapter IX of David Hilbert's book Die Theorie der algebraischen Zahlkorper. In this chapter, the title is Die Zahlringe des Korpers, meaning the number rings of the field. This word is derived from Zahlring. A ring is one of the primary algebraic structures utilized in abstract algebra. It comprises a set paired with two binary operations that broaden the arithmetic operations of addition and multiplication. Through this broadening, arithmetic theorems are extended to non-numerical objects such as polynomials, series, matrices, and functions. A ring acts as an abelian group under one operation and also possesses another operation which is associative, distributive over the first group's operation, and has an identity element - except by some definitions. Abstract algebra theory has numerous branches of mathematics greatly impacted. These areas encompass problems that naturally arise from algebraic number theory, algebraic geometry.