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). 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) (which is itself quite different from the algebraic-geometry sense https://en.wikipedia.org/wiki/Algebraic_variety). See, for example, https://math.stackexchange.com/questions/3756136/why-is-the-... .