Spectral Topology on MV-Modules

F. Forouzesh, E. Eslami () and A. Borumand Saeid ()
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F. Forouzesh: Faculty of Mathematics and Computing, Higher Education Complex of Bam, Kerman, Iran
E. Eslami: Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
A. Borumand Saeid: Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

New Mathematics and Natural Computation (NMNC), 2015, vol. 11, issue 01, 13-33

Abstract: In this paper, the spectral topology and quasi-spectral topology of proper primeA-ideals in anMV-module are introduced. We show that the spectral topology of proper ⋅-prime ideals of aPMV-algebra with unity for product, is the same as the spectral topology of proper prime ideals in anMV-algebra. Also we show that the set of all primeA-ideals in anMV-module with spectral topology is notT0andT1topological spaces but quasi-spectral topology isT0-space and is notT1-space. Finally, we investigate when the set of all primeA-ideals in anMV-module are Hausdorff and disconnected.

Keywords: MV-modules; primeA-ideal; spectrum; spectral topology; quasi-spectral topology (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S1793005715500027

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