> Interesting, I never realized that fields weren't algebras! One has to be quite careful with the terminology when crossing disciplines, as here. Fields are,

> Interesting, I never realized that fields weren't algebras! One has to be quite careful with the terminology when crossing disciplines, as here. Fields are, rather boringly, algebras over themselves, in what I dare to call the ‘usual’ sense of an algebra over a field (https://en.wikipedia.org/wiki/Algebra_over_a_field https://en.wikipedia.org/wiki/Algebra_over_a_field). Rather what hither_shores is saying is that the collection of fields does not form a variety of algebras, in the sense of universal algebra https://en.wikipedia.org/wiki/Variety_(universal_algebra) https://en.wikipedia.org/wiki/Variety_(universal_algebra) (which is itself quite different from the algebraic-geometry sense https://en.wikipedia.org/wiki/Algebraic_variety https://en.wikipedia.org/wiki/Algebraic_variety). See, for example, https://math.stackexchange.com/questions/3756136/why-is-the-category-of-fields-seemingly-so-poorly-behaved#comment7727407_3756136 https://math.stackexchange.com/questions/3756136/why-is-the-... .