ON THE ALGEBRAIC DIMENSION OF RIESZ SPACES.

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. [ABSTRACT FROM AUTHOR]