Division Ring

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division ring

[di′vizh·ən ‚riŋ]
A ring in which the set of nonzero elements form a group under multiplication.
More generally, a nonassociative ring with nonzero elements in which, for any two elements a and b, there are elements x and y such that ax = b and ya = b.

Division Ring


a set of elements for which operations of addition, subtraction, multiplication, and division are defined that have the usual properties of the operations on numbers, except that the operation of multiplication need not be commutative. The set of quaternions is an example of a division ring. If multiplication of elements of a division ring is commutative, the division ring is a field.

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