CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This article is about an algebraic structure. For geometric rings, see Annulus (mathematics) . For the set theory concept, see Ring of sets . Chapter IX of David Hilbert 's Die Theorie der algebraischen Zahlkörper. The chapter title is Die Zahlringe des Körpers, literally "the number rings of the field". The word "ring" is the contraction of "Zahlring". In mathematics , and more specifically in algebra , a ring is an algebraic structure with operations that generalize the arithmetic operations of addition and multiplication . Through this generalization, theorems from arithmetic are extended to non-numerical objects like polynomials , series , matrices and functions . Rings were first formalized as a common generalization of Dedekind domains that occur in number theory , and of pol...