New Kind of MV-Modules

Abstract

In this paper, by considering the notion of MV-modules, which is the structure that naturally correspond to lu-modules over lu-rings, we investigate some properties of a new kind of MV-modules, that we introduced in Borzooei and Saidi Goraghani, Free MV-modules, J. Intell. Fuzzy Syst. 31 (2016), 151–161 as Ak-modules. With the current situation, it was not easy for us to work on some concepts such as free MV-modules and Noetherian MV-modules. So we limited our scope of work by introducing a new kind of MV-modules. We define and study the notions of free Ak-modules, radical of Ak-modules and Noetherian Ak-modules, where A is a product MV-algebra and k∈ℕ. For example, we state a general representation for a free Ak-module, and we obtain conditions in which an Ak-module can be Noetherian.

Keywords

• MV-algebra
• PMV-algebra
• Ak-module
• Free Ak-module
• Radical of an Ak-module
• Noetherian Ak-module