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Ring (mathematics) - Wikipedia

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In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. Informally, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. Ring elements may be numbers such as integers or complex numbers, but they may also be non-numerical objects such as polynomials, square matrices, functions, and power series. Formally, a ring is a set endowed with two binary operations called addition and multiplication such that the ring is an abelian group with respect to the addition operator, and the multiplication operator is associative, is distributive over the addition operation, and has a multiplicative identity element. (Some authors define rings without requiring a multiplicative identity and instead call the structure defined above a ring with identity. See § Variations on the definition.) Whether a ring is commutative has pr

Ring (mathematics) - Wikipedia Jump to content From Wikipedia, the free encyclopedia Algebraic structure with addition and multiplication This article is about the algebraic structure. For other uses in mathematics, see Ring (disambiguation) § Mathematics . Algebraic structure → Ring theory Ring theory Basic concepts Rings • Subrings • Ideal • Quotient ring • Fractional ideal • Total ring of fractions • Product of rings • Free product of associative algebras • Tensor product of algebras Ring homomorphisms • Kernel • Inner automorphism • Frobenius endomorphism Algebraic structures • Module • As

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