On the algebraic dimension of Riesz spaces - N. M. Baziv; O. B. Hrybel (Математичні Студії)
We prove that the algebraic dimension of an infinite dimensional $C$-$σ$-complete Riesz space (in particular, of a Dedekind $σ$-complete and a laterally $σ$-complete Riesz space) with the principal projection property which either has a weak order unit or is not purely atomic, is at least continuum. A similar (incomparable to ours) result for complete metric linear spaces is well known.