Free MV-Modules

Article type: Research Article

Authors: Borzooei, R.A.^{a; *} | Goraghani, S. Saidi^b

Affiliations: [a] Department of Mathematics, Shahid Beheshti University, Tehran, Iran | [b] Department of Mathamatics, Farhangian University, Kerman, Iran

Correspondence: [*] Corresponding author. R.A. Borzooei, Department of Mathematics, Shahid Beheshti University, Tehran, Iran. Tel.: +989124903982; Fax: +982122431652; E-mail: [email protected].

Abstract: In this paper, by considering the notion of MV-modules, which is the structure that naturally correspond tolu-modules over lu-rings, we present the definitions of finitely generated and free MV-modules. Also, we define the notions of Ak-module and free Ak-module, where A is a PMV-algebra and k∈ℕ. In a special case, we obtain a general representation for a free Ak-module. In the follow, by considering the notion of free objects, we obtain a method to construct a free objecton a nonempty set in Ak-modules. Finally, we present the definitions of invariant dimension property and Ak-invariant dimension property in PMV-algebras and prove that every PMV-algebra has the Ak-invariant dimension property.

Keywords: (MV, PMV)-algebra, MV-module, free MV-module, invariant dimension property.

DOI: 10.3233/IFS-162128

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 1, pp. 151-161, 2016