Definition:Division Ring/Also known as
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Division Ring: Also known as
Some sources use division ring as the definition of a field.
However, this is non-standard: it is usually specified that a field product has to be commutative.
Some sources refer to a division ring as a skew field, but the latter is usually applied to a division ring whose ring product is specifically non-commutative.
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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): division ring (skew field)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): division ring (skew field)