Spectral Topology on MV-Modules

In this paper, the spectral topology and quasi-spectral topology of proper prime A-ideals in an MV-module are introduced. We show that the spectral topology of proper (.)- prime ideals of a PMV-algebra with unity for product, is the same as the spectral topology of proper prime ideals in an MV-algebra. Also we show that the set of all prime A-ideals in an MV-module with spectral topology is not T-0 and T-1 topological spaces but quasi-spectral topology is T-0-space and is not T-1-space. Finally, we investigate when the set of all prime A-ideals in an MV- module are Hausdorff and disconnected.