Research article new kind of mv-modules

S. Saidi Goraghani; R. A. Borzooei; S. S. Ahn; Y. B. Jun

doi:10.2991/ijcis.d.200602.001

Research article new kind of mv-modules

S. Saidi Goraghani, R. A. Borzooei, S. S. Ahn, Y. B. Jun

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	794-801
Number of pages	8
Journal	International Journal of Computational Intelligence Systems
Volume	13
Issue number	1
DOIs	https://doi.org/10.2991/ijcis.d.200602.001
State	Published - 2020

Keywords

A-module
Free A-module
MV-algebra
Noetherian A-module
PMV-algebra
Radical of an A-module

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10.2991/ijcis.d.200602.001

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@article{d078c80f1bd841be9519627edb0c4ea7,

title = "Research article 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 = "A-module, Free A-module, MV-algebra, Noetherian A-module, PMV-algebra, Radical of an A-module",

author = "Goraghani, {S. Saidi} and Borzooei, {R. A.} and Ahn, {S. S.} and Jun, {Y. B.}",

note = "Publisher Copyright: {\textcopyright} 2020 The Authors. Published by Atlantis Press SARL.",

year = "2020",

doi = "10.2991/ijcis.d.200602.001",

language = "English",

volume = "13",

pages = "794--801",

journal = "International Journal of Computational Intelligence Systems",

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T1 - Research article new kind of mv-modules

AU - Goraghani, S. Saidi

AU - Borzooei, R. A.

AU - Ahn, S. S.

AU - Jun, Y. B.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - A-module

KW - Free A-module

KW - MV-algebra

KW - Noetherian A-module

KW - PMV-algebra

KW - Radical of an A-module

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U2 - 10.2991/ijcis.d.200602.001

DO - 10.2991/ijcis.d.200602.001

M3 - Article

AN - SCOPUS:85089223182

SN - 1875-6891

VL - 13

SP - 794

EP - 801

JO - International Journal of Computational Intelligence Systems

JF - International Journal of Computational Intelligence Systems

IS - 1

ER -

Research article new kind of mv-modules

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