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- In mathematics, a ring is an algebraic structure that generalizes fields1. A ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers12. The two binary operations are commonly interpreted as addition and multiplication, respectively2. The properties that the binary operations must satisfy include additive associativity, additive commutativity, additive identity, and distributivity of multiplication over addition2.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers.
en.wikipedia.org/wiki/Ring_(mathematics)A ring in the mathematical sense is a set together with two binary operators and (commonly interpreted as addition and multiplication, respectively) satisfying the following conditions: 1. Additive associativity: For all , , 2. Additive commutativity: For all , , 3. Additive identity: There exists an element such that for all , , 4.
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