New Kind of MV-Modules

Authors

S. Saidi Goraghani¹, R.A. Borzooei^2, , S.S. Ahn^{3, *,} , Y.B. Jun^{2, 4}

¹Department of Mathematics, Farhangian University, Tehran, Iran

²Department of Mathematics, Shahid Beheshti University, Tehran, Iran

³Department of Mathematics Education, Dongguk University, Seoul, Korea

⁴Department of Mathematics Education, Gyeongsang National University, Jinju, Korea

^*Corresponding author. Email: sunshine@dongguk.edu

DOI

10.2991/ijcis.d.200602.001How to use a DOI?

Keywords

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

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 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∈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.

Copyright

© 2020 The Authors. Published by Atlantis Press SARL.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - S. Saidi Goraghani
AU  - R.A. Borzooei
AU  - S.S. Ahn
AU  - Y.B. Jun
PY  - 2020
DA  - 2020/06/18
TI  - New Kind of MV-Modules
JO  - International Journal of Computational Intelligence Systems
SP  - 794
EP  - 801
VL  - 13
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.200602.001
DO  - 10.2991/ijcis.d.200602.001
ID  - Goraghani2020
ER  -