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In mathematics, more specifically modern algebra and ring theory, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exists a and b in R with a·b ≠ b·a. Note that many authors use the term noncommutative ring to refer to rings which are not necessarily commutative, and hence include commutative rings in their definition.

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  • In mathematics, more specifically modern algebra and ring theory, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exists a and b in R with a·b ≠ b·a. Note that many authors use the term noncommutative ring to refer to rings which are not necessarily commutative, and hence include commutative rings in their definition.
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