VerSSsace Earrings 74 3D print model

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A ring is one of the basic structures used in abstract algebra, which generalizes arithmetic operations. It consists of a set with two binary operations: addition and multiplication. Addition and multiplication in a ring generalize the arithmetic operations from arithmetic theory to other objects such as polynomials, series, matrices, and functions. An abelian group's identity element makes a ring one, where the group's operation is called addition, and the second operation is multiplication. The distribution property applies over an abelian group's operation, which is also associative. Rings can be either commutative or non-commutative depending on how they perform operations under different conditions. Commutative algebra examines this area of ring theory, with major contributions coming from algebraic number theory and geometry. Integers form a set with two arithmetic operations. So do polynomials and rings from coordinates. Noncommutative examples include matrix spaces, representation group rings, and differential operators in functional analysis, among others. Dedekind first conceptualized the ring around 1870; contributions to formalize this theory continued through 1920. This included contributions by Hilbert, Fraenkel, Noether.