Undergrad Difference between an Algebra and a Vector space

[Milsomonk]

Hi guys,
I am a little confused on the difference between an Algebra and a vector space. I´m guessing there´s a fairly simple distinction. Any guidance would be much appreciated, I accept both hand wavy and hardcore axiom based responses :)
Cheers

 

[fresh_42]

Hi guys,
I am a little confused on the difference between an Algebra and a vector space. I´m guessing there´s a fairly simple distinction. Any guidance would be much appreciated, I accept both hand wavy and hardcore axiom based responses :)
Cheers

An algebra is a vector space, on which additionally a second binary operation, usually referred to as multiplication is defined.

 

[Milsomonk]

Amazing, thanks :)