What is the multiplicative identity element in a field?

Conditions

• The context is the second condition of the field definition (multiplicative abelian group).
• The element 1 must be in F - {0}.

Reasoning, step by step

1. Identify the requirement for a multiplicative identity in the abelian group F - {0}.
2. Note that the speaker explicitly states 'multiplicative identity I mean one belongs to F'.
3. Understand that 1 is distinct from the additive identity 0.
4. Conclude that 1 serves as the identity element for multiplication in the field.

Example

The speaker states 'multiplicative identity I mean one belongs to F' while explaining the properties required for F - {0} to be an abelian group under multiplication.

Common misconceptions

• Confusing the multiplicative identity 1 with the additive identity 0.
• Assuming that the multiplicative identity can be zero.

Watch the explanation

Explore next

• Why does the lecturer say that 0 belongs to F in the additive group condition?
• What are the five properties required for F - {0} to be an abelian group under multiplication?