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Ring theory: Difference between revisions
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(Created page with "== Introduction == Ring theory is a branch of abstract algebra that studies algebraic structures known as rings. The concept of a ring was first formulated by mathematician Richard Dedekind in 1882. The theory has applications in various fields of mathematics, including number theory, algebraic geometry, and combinatorics. == Definition == A ring is a set R equipped with two binary operations, addition and multiplication, that satisfy certain axio...") |
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A ring is a set R equipped with two binary operations, addition and multiplication, that satisfy certain axioms. These axioms include associativity of addition and multiplication, distributivity of multiplication over addition, and the existence of an additive identity and additive inverses. Some rings also have a multiplicative identity, but this is not required in the general definition. | A ring is a set R equipped with two binary operations, addition and multiplication, that satisfy certain axioms. These axioms include associativity of addition and multiplication, distributivity of multiplication over addition, and the existence of an additive identity and additive inverses. Some rings also have a multiplicative identity, but this is not required in the general definition. | ||
[[Image:Detail-77739.jpg|thumb|center|A set of mathematical symbols and equations representing the operations in a ring.]] | |||
== Types of Rings == | == Types of Rings == | ||