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Ring theory: Difference between revisions
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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.]] | [[Image:Detail-77739.jpg|thumb|center|A set of mathematical symbols and equations representing the operations in a ring.|class=only_on_mobile]] | ||
[[Image:Detail-77740.jpg|thumb|center|A set of mathematical symbols and equations representing the operations in a ring.|class=only_on_desktop]] | |||
== Types of Rings == | == Types of Rings == | ||