Algebra over a field ↩

shorthands: {}
aliases: [Algebra]
created: 2022-01-09 15:48:18
modified: 2022-01-11 15:42:49

Which distributes over vector addition:

And for it satisfies:

Unit element

The algebra has a unit element if there is an element which acts as a left and right multiplicative identity:

Associative algebra

The algebra is associative if its multiplication is associative:

Examples

• is an algebra with unit element
• is an algebra with unit element
• Any field is an algebra with unit element, but an algebra with unit element is not necessarily a field since it may have nonzero elements that do not have a multiplicative inverse