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In mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. This distinction results from the high number of fundamental properties of commutative rings that do not extend to noncommutative rings.
Commutative rings appear in the following chain of class inclusions:
Gallery (5)
Connections
ideal
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continuous function
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modular arithmetic
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module
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Lie algebra
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p-adic number
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sheaf
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noetherian ring
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field of fractions
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quotient ring
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formal power series
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spectrum of a ring
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topological ring
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trivial ring
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non-associative algebra
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integrally closed domain
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finitely generated module
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noncommutative ring
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German
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mathematics
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