We study the R-modules M which are finitely generated, quasi-projective and self-generator (briefly called $${{\mathrm{FQS}}}$$ modules). We extend some basic results from semiprime rings to semiprime $${{\mathrm{FQS}}}$$ modules. In particular, we show that any semiprime $${{\mathrm{FQS}}}$$ module with Krull dimension is a Goldie module. We also show that every $${{\mathrm{FQS}}}$$ module with Krull dimension has only finitely many minimal prime submodules. Consequently, if M is an $${{\mathrm{FQS}}}$$ module with Krull dimension, then $$\text{ k-dim }\,M$$ is equal to $$\text{ k-dim }\,\frac{M}{P}$$ for some prime submodule P of M. Moreover, we observe that an $${{\mathrm{FQS}}}$$ module has the classical Krull dimension if and only if it satisfies ACC on prime submodules. Finally, we prove that a semiprime $${{\mathrm{FQS}}}$$ module M is $$\alpha $$ -short if and only if $$\text{ n-dim }\, M =\alpha ,$$ where $$\alpha \ge 0.$$