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), 151161 as A(k)-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 A(k)-modules, radical of A(k)-modules and Noetherian A(k)-modules, where A is a product MV-algebra and k is an element of N. For example, we state a general representation for a free A(k)-module, and we obtain conditions in which an A(k)-module can be Noetherian. (C) 2020 The Authors. Published by Atlantis Press SARL.