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: borzooei@sbu.ac.ir.
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.
