Units of an associative algebra form a group

Metadata
aliases: []
shorthands: {}
created: 2021-11-14 00:01:43
modified: 2022-01-10 04:13:04

Statement: Let be an associative algebra with unit element . Then the set of all units in form a group under multiplication.

Proof

Being associative is given, every element has an inverse since they are all units and acts as identity (neutral element).