  In this paper we present the definition of quasi-bases for modules over a
ring that is commutative but not necessarily division and discuss properties
that guarantee the existence of quasi-bases. Based on this result we further
prove that every finitely generated module over $L^{0}(\mathcal{F},K)$ has a
quasi-basis, where $K$ is the scalar field of real numbers or complex numbers
and $L^{0}(\mathcal{F},K)$ is the algebra of equivalence classes of $K$--valued
random variables defined on a probability space $(\Omega,\mathcal{F},P)$.
