Definition talk:Algebra over Ring

Algebra vs Algebraic Structure
If I understand correctly, eventually all such uses of "algebra" will have to be renamed as "algebraic structure". Even though there is not much action here at the moment, this is the ultimate goal, right?--Julius (talk) 00:57, 21 February 2023 (UTC)


 * On the contrary. An "algebraic structure" is precisely defined as a set with a number of operations on it (either 1 or 2 usually, but not necessarily limited to that). Hence a semigroup, group, ring and field are all algebraic structures. An "algebra" is also precisely defined as a module (itself constructed as it is with an underlying algebraic structure with an operation on that) with yet another (bilinear) operation on that too. --prime mover (talk) 06:38, 21 February 2023 (UTC)