ring, in mathematics, system consisting of a set R of elements and two binary operations, such that addition makes R a commutative group and multiplication is associative and distributes over addition (see commutative law ; associative law ; distributive law ). A commutative ring is one in which the commutative law also holds for multiplication. Examples of commutative rings are the sets of integers (see number ) and real numbers. Square matrices (see matrix ) furnish examples of non-communtative rings.
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