Definition:Field Zero

Definition

Let $\struct {F, +, \times}$ be a field.

The identity for field addition is called the field zero (of $\struct {F, +, \times}$).

It is denoted $0_F$ (or just $0$ if there is no danger of ambiguity).

Also known as

When it is clear and unambiguous what is being discussed, the field zero is often called just the zero.

In the context of number fields, the field zero can also be referred to as the additive identity.

Also see

• In Field Product with Zero, it is shown that the field zero is a zero element for the field product, thereby justifying its name as the zero of the field.

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
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $0$ Zero
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $0$ Zero
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): additive identity
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): zero: 2a.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): additive identity
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): additive identity