Affiliations: [a] Faculty of Mathematics and Computing, Department of Math, Higher Education Complex of Bam, Iran | [b] Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Correspondence:
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Corresponding author. Arsham Borumand Saeid, Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. Tel.: +98 34 32312490; E-mail: [email protected].
Abstract: In this paper, we introduce the notion of ·-primary ideals in PMV-algebras and primary A-ideals in MV-modules. Then we study primary decomposition of an ideal in an MV-algebra and primary decomposition of an A-ideal in an MV-module. Finally, we show that if an ideal in MV-algebras has a primary decomposition, then this decomposition may not be a reduced primary decomposition and if an A-ideal in an MV-module has a primary decomposition, then this decomposition may not be a reduced primary decomposition. We show that if an A-ideal I of an MV-module M has a reduced primary decomposition and this decomposition is unique.
