Definition:Field (Abstract Algebra)/Also defined as
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Field: Also defined as
Some sources do not insist that the field product of a field is commutative.
That is, what they define as a field, $\mathsf{Pr} \infty \mathsf{fWiki}$ defines as a division ring.
When they wish to refer to a field in which the field product is commutative, the term commutative field is used.
Sources
- 1944: Emil Artin and Arthur N. Milgram: Galois Theory (2nd ed.) (translated by Arthur N. Milgram) ... (previous) ... (next): $\text I$. Linear Algebra: $\text A$. Fields
- 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Algebraic Concepts