Field ↩

shorthands: {}
aliases: [field]
created: 2021-11-05 23:02:27
modified: 2022-01-10 04:13:04

1. is an abelian group under and the identity element for is denoted by
2. Multiplication distributes over addition:

3. is an abelian group under multiplication and the identity element is written as 1

Examples

• Rational numbers
• Real numbers
• Complex numbers

Comments

• The additive identity of a field is a multiplicative annihilator
• A field has at least two elements
• The product of two nonzero field elements is nonzero