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field, in algebra

field, in algebra, set of elements (usually numbers) that may be combined under the operations of addition and multiplication so that it constitutes an additive group, the nonzero elements form a multiplicative group, and multiplication distributes over addition. The set of real numbers (see number) and the set of complex numbers are both examples of fields.

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2024, Columbia University Press. All rights reserved.

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