We study the R-modules M which are finitely generated, quasi-projective and self-generator (briefly called FQS\documentclass[12pt]{minimal}
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\begin{document}$${{\mathrm{FQS}}}$$\end{document} modules). We extend some basic results from semiprime rings to semiprime FQS\documentclass[12pt]{minimal}
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\begin{document}$${{\mathrm{FQS}}}$$\end{document} modules. In particular, we show that any semiprime FQS\documentclass[12pt]{minimal}
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\begin{document}$${{\mathrm{FQS}}}$$\end{document} module with Krull dimension is a Goldie module. We also show that every FQS\documentclass[12pt]{minimal}
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\begin{document}$${{\mathrm{FQS}}}$$\end{document} module with Krull dimension has only finitely many minimal prime submodules. Consequently, if M is an FQS\documentclass[12pt]{minimal}
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\begin{document}$${{\mathrm{FQS}}}$$\end{document} module with Krull dimension, then k-dimM\documentclass[12pt]{minimal}
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\begin{document}$$\text{ k-dim }\,M$$\end{document} is equal to k-dimMP\documentclass[12pt]{minimal}
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\begin{document}$$\text{ k-dim }\,\frac{M}{P}$$\end{document} for some prime submodule P of M. Moreover, we observe that an FQS\documentclass[12pt]{minimal}
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\begin{document}$${{\mathrm{FQS}}}$$\end{document} module has the classical Krull dimension if and only if it satisfies ACC on prime submodules. Finally, we prove that a semiprime FQS\documentclass[12pt]{minimal}
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\begin{document}$${{\mathrm{FQS}}}$$\end{document} module M is α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}-short if and only if n-dimM=α,\documentclass[12pt]{minimal}
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\begin{document}$$\text{ n-dim }\, M =\alpha ,$$\end{document} where α≥0.\documentclass[12pt]{minimal}
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\begin{document}$$\alpha \ge 0.$$\end{document}
