x_{\gamma}(-j) \ \vert j \in {\mathbb{N}}, \gamma \in \Gamma \}$ factors. We call such basis also *a monomial basis*.

This paper is organized as follows: in Sections \[algebra\] - \[spinor\] we give the setting. In Section \[feigin\] we define the Feigin-Stoyanovsky subspace and monomial ordering on the set of monomials.

In Sections \[uvjeti\_razlike\] - \[kraj1\] we first study $W(\Lambda)$ when $\Lambda$ is of level 1. By Poincaré-Birkhoff-Witt’s theorem the set of *monomial vectors* $$\begin{aligned}
\label{spanning}
\{ \ x_{\beta_{1}}(-j_1) \dots x_{\beta_{r}}(-j_r)v_{\Lambda} \ \vert \ \beta_{i} \in \Gamma, r \in {\mathbb{Z}}_+, j_r \in {\mathbb{N}}\ \}\end{aligned}$$ spans $W(\Lambda)$. We reduce set using the relations between vertex operators. We express the smallest element with regard to the linear ordering we established in \[order\] as the sum of the greater ones. Therefore this smallest element can be excluded from the spanning set . The elements that do not contain this smallest monomials are said to satisfy so-called difference and initial conditions on $W(\Lambda)$. Such elements span $W(\Lambda)$. In Section \[kraj1\] we show their linear independence and it follows these monomials form a basis of the Feigin-Stoyanovsky’s type subspace. In the proof of the linear independence, we use the operators which commute with the action of 