@rtn@chaos.social - in modern math, an 'associative algebra' is a structure where you can add, subtract, and multiply, obeying certain rules - for example, that multiplication is associative. Often we call this simply an 'algebra'. But a 'Lie algebra' is a different kind of thing, where you can add, subtract, and take the 'bracket' of two elements, obeying some other rules. And then there are other things, like 'nonassociative algebras'. All these are examples of 'algebraic structures': sets with some operations obeying some identities. Other examples are 'groups', 'vector spaces', etc. All these structures are studied in the branch of math called 'abstract algebra', or often just 'algebra'. Yes, this is a different use of the word 'algebra' from the one I mentioned at first! And of course it's different from the kind of 'algebra' we learn as kids - it's much more general. Wikipedia is not bad at explaining the big picture: https://en.wikipedia.org/wiki/Algebra They distinguish between 'abstract algebra' and 'elementary algebra', the kind we learn as kids. I spend a lot of time studying abstract algebra, because it goes on and on and on and it's very beautiful.