Hi all, I'm trying to understand the structure of an "algebra over a field".
The definition I get from wolfram is
"Formally, an algebra is a vector space V over a field F with a multiplication."
So if I was to break down this down....
A vector space has two operations
+:V x V --> V (addition)
. :F x V --> V
and so if A was an algebra over F, would it mean it has three operations?
+:A x A --> A (addition)
. :A x V --> A
* : A x A --> A (multiplication)