> I never knew that anyone referred to any generic set with operations as an "algebra". That's a magma! An algebra has much more structure than any generic set

> I never knew that anyone referred to any generic set with operations as an "algebra". That's a magma! An algebra has much more structure than any generic set with operations. I think this comes from competing definitions of the term 'algebra'. There's what, for want of anything better than the terrible term, I'll call the 'algebraist's algebra', which is (at least) a ring that is compatibly a module over some other ring; and there's what, as smadge (https://news.ycombinator.com/item?id=21443587 https://news.ycombinator.com/item?id=21443587) mentions, could be called the 'universal algebraist's algebra', which is a model for a certain signature, of which the algebraist's algebra is just one special case. EDIT: I see that matt_noonan (https://news.ycombinator.com/item?id=21443892 https://news.ycombinator.com/item?id=21443892) made this point several hours ago, but I leave this post in case the links below are convincing. For sources maybe more authoritative than Wikipedia, you might consult Springer's Encyclopedia of Mathematics (https://www.encyclopediaofmath.org/index.php/Variety_of_universal_algebras https://www.encyclopediaofmath.org/index.php/Variety_of_univ...) or the nLab (https://ncatlab.org/nlab/show/universal+algebra https://ncatlab.org/nlab/show/universal+algebra).