Characterization of Derived Nilpotent (Engel) Lie Ring of Fuzzy Hyperrings by Using Fuzzy Strongly Regular Relations

E. Mohammadzadeh; R. A. Borzooei; F. Mohammadzadeh; S. S. Ahn

doi:10.1080/16168658.2022.2152883

Characterization of Derived Nilpotent (Engel) Lie Ring of Fuzzy Hyperrings by Using Fuzzy Strongly Regular Relations

E. Mohammadzadeh
, R. A. Borzooei
, F. Mohammadzadeh
, S. S. Ahn

Department of Mathematics Education

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

Abstract

In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation (Formula presented.) ((Formula presented.)). Moreover, we proved that for a fuzzy hyperring S, the quotient (Formula presented.) ((Formula presented.)) was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of ζ. Also, we studied the relationship between the strongly regular relation and ζ-role of a given fuzzy hyperring.

Original language	English
Pages (from-to)	407-424
Number of pages	18
Journal	Fuzzy Information and Engineering
Volume	14
Issue number	4
DOIs	https://doi.org/10.1080/16168658.2022.2152883
State	Published - 2022

Keywords

(Nilpotent) Lie ring
Engel Lie ring
fuzzy hyperring
strongly regular relation

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10.1080/16168658.2022.2152883

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title = "Characterization of Derived Nilpotent (Engel) Lie Ring of Fuzzy Hyperrings by Using Fuzzy Strongly Regular Relations",

abstract = "In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation (Formula presented.) ((Formula presented.)). Moreover, we proved that for a fuzzy hyperring S, the quotient (Formula presented.) ((Formula presented.)) was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of ζ. Also, we studied the relationship between the strongly regular relation and ζ-role of a given fuzzy hyperring.",

keywords = "(Nilpotent) Lie ring, Engel Lie ring, fuzzy hyperring, strongly regular relation",

author = "E. Mohammadzadeh and Borzooei, \{R. A.\} and F. Mohammadzadeh and Ahn, \{S. S.\}",

note = "Publisher Copyright: {\textcopyright} 2022 The Authors. Published by Taylor \& Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society, Guangdong Province Operations Research Society of China.",

year = "2022",

doi = "10.1080/16168658.2022.2152883",

language = "English",

volume = "14",

pages = "407--424",

journal = "Fuzzy Information and Engineering",

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publisher = "Tsinghua University Press",

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TY - JOUR

T1 - Characterization of Derived Nilpotent (Engel) Lie Ring of Fuzzy Hyperrings by Using Fuzzy Strongly Regular Relations

AU - Mohammadzadeh, E.

AU - Borzooei, R. A.

AU - Mohammadzadeh, F.

AU - Ahn, S. S.

N1 - Publisher Copyright: © 2022 The Authors. Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society, Guangdong Province Operations Research Society of China.

PY - 2022

Y1 - 2022

N2 - In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation (Formula presented.) ((Formula presented.)). Moreover, we proved that for a fuzzy hyperring S, the quotient (Formula presented.) ((Formula presented.)) was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of ζ. Also, we studied the relationship between the strongly regular relation and ζ-role of a given fuzzy hyperring.

AB - In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation (Formula presented.) ((Formula presented.)). Moreover, we proved that for a fuzzy hyperring S, the quotient (Formula presented.) ((Formula presented.)) was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of ζ. Also, we studied the relationship between the strongly regular relation and ζ-role of a given fuzzy hyperring.

KW - (Nilpotent) Lie ring

KW - Engel Lie ring

KW - fuzzy hyperring

KW - strongly regular relation

UR - https://www.scopus.com/pages/publications/85144836834

U2 - 10.1080/16168658.2022.2152883

DO - 10.1080/16168658.2022.2152883

M3 - Article

AN - SCOPUS:85144836834

SN - 1616-8658

VL - 14

SP - 407

EP - 424

JO - Fuzzy Information and Engineering

JF - Fuzzy Information and Engineering

IS - 4

ER -

Characterization of Derived Nilpotent (Engel) Lie Ring of Fuzzy Hyperrings by Using Fuzzy Strongly Regular Relations

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Keywords

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