Stabilizer theory in MV-algebras

Article type: Research Article

Authors: Forouzesh, Fereshteh | Eslami, Esfandiar | Borumand Saeid, Arsham

Affiliations: Department of Mathematics, Higher Education Complex of Bam, Iran | Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

Note: [] Corresponding author. Arsham Borumand Saeid, Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran. Tel: +98 341 3202490; Fax: +98 341 3221080; E-mails: arsham@uk.ac.ir (Arsham Borumand Saeid); frouzesh@bam.ac.ir (Fereshteh Forouzesh); esfandiar.eslami@uk.ac.ir (Esfandiar Eslami).

Abstract: In this paper, we introduce two different stabilizers of X with respect to Y for subsets X and Y of an MV-algebra A. We show that stabilizers are ideals and we investigate the relation between stabilizers and some other ideals in MV-algebras. We also show that if I and J are ideals in an MV-algebra A, then the stabilizer of I with respect to J is the relative pseudo-complement of I with respect to J in the lattice of ideals of A.

Keywords: MV-algebra, stabilizer, ideal

DOI: 10.3233/IFS-141122

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 3, pp. 1557-1565, 2014