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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 A_k-module and free A_k-module, where A is a PMV-algebra and $k \in ℕ$ . In a special case, we obtain a general representation for a free A_k-module. In the follow, by considering the notion of free objects, we obtain a method to construct a free objecton a nonempty set in A_k-modules. Finally, we present the definitions of invariant dimension property and A_k-invariant dimension property in PMV-algebras and prove that every PMV-algebra has the A_k-invariant dimension property.

Keywords

invariant dimension property.

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Free MV -Modules

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