(⊙ , ∨) -Derivations on MV-algebras

Xueting Zhao; Aiping Gan; Yichuan Yang

doi:10.1007/s00500-023-09384-2

(⊙ , ∨) -Derivations on MV-algebras

Xueting Zhao
, Aiping Gan
, Yichuan Yang^*

^*Corresponding author for this work

School of Mathematical Sciences

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

1 Scopus citations

Abstract

Let A be an MV-algebra. An (⊙ , ∨) -derivation on A is a map d: A→ A satisfying: d(x⊙ y) = (d(x) ⊙ y) ∨ (x⊙ d(y)) for all x, y∈ A . This paper initiates the study of (⊙ , ∨) -derivations on MV-algebras. Several families of (⊙ , ∨) -derivations on an MV-algebra are explicitly constructed to give realizations of the underlying lattice of an MV-algebra as lattices of (⊙ , ∨) -derivations. Furthermore, (⊙ , ∨) -derivations on a finite MV-chain are enumerated and the underlying lattice is described.

Original language	English
Pages (from-to)	1833-1849
Number of pages	17
Journal	Soft Computing
Volume	28
Issue number	3
DOIs	https://doi.org/10.1007/s00500-023-09384-2
State	Published - Feb 2024

Keywords

Boolean center
Complete lattice
Derivation
Direct product
Fixed point set
Ideal
MV-algebra

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title = "(⊙ , ∨) -Derivations on MV-algebras",

abstract = "Let A be an MV-algebra. An (⊙ , ∨) -derivation on A is a map d: A→ A satisfying: d(x⊙ y) = (d(x) ⊙ y) ∨ (x⊙ d(y)) for all x, y∈ A . This paper initiates the study of (⊙ , ∨) -derivations on MV-algebras. Several families of (⊙ , ∨) -derivations on an MV-algebra are explicitly constructed to give realizations of the underlying lattice of an MV-algebra as lattices of (⊙ , ∨) -derivations. Furthermore, (⊙ , ∨) -derivations on a finite MV-chain are enumerated and the underlying lattice is described.",

keywords = "Boolean center, Complete lattice, Derivation, Direct product, Fixed point set, Ideal, MV-algebra",

author = "Xueting Zhao and Aiping Gan and Yichuan Yang",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2024",

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doi = "10.1007/s00500-023-09384-2",

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volume = "28",

pages = "1833--1849",

journal = "Soft Computing",

issn = "1432-7643",

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TY - JOUR

T1 - (⊙ , ∨) -Derivations on MV-algebras

AU - Zhao, Xueting

AU - Gan, Aiping

AU - Yang, Yichuan

PY - 2024/2

Y1 - 2024/2

N2 - Let A be an MV-algebra. An (⊙ , ∨) -derivation on A is a map d: A→ A satisfying: d(x⊙ y) = (d(x) ⊙ y) ∨ (x⊙ d(y)) for all x, y∈ A . This paper initiates the study of (⊙ , ∨) -derivations on MV-algebras. Several families of (⊙ , ∨) -derivations on an MV-algebra are explicitly constructed to give realizations of the underlying lattice of an MV-algebra as lattices of (⊙ , ∨) -derivations. Furthermore, (⊙ , ∨) -derivations on a finite MV-chain are enumerated and the underlying lattice is described.

AB - Let A be an MV-algebra. An (⊙ , ∨) -derivation on A is a map d: A→ A satisfying: d(x⊙ y) = (d(x) ⊙ y) ∨ (x⊙ d(y)) for all x, y∈ A . This paper initiates the study of (⊙ , ∨) -derivations on MV-algebras. Several families of (⊙ , ∨) -derivations on an MV-algebra are explicitly constructed to give realizations of the underlying lattice of an MV-algebra as lattices of (⊙ , ∨) -derivations. Furthermore, (⊙ , ∨) -derivations on a finite MV-chain are enumerated and the underlying lattice is described.

KW - Boolean center

KW - Complete lattice

KW - Derivation

KW - Direct product

KW - Fixed point set

KW - Ideal

KW - MV-algebra

UR - https://www.scopus.com/pages/publications/85181880114

U2 - 10.1007/s00500-023-09384-2

DO - 10.1007/s00500-023-09384-2

M3 - 文章

AN - SCOPUS:85181880114

SN - 1432-7643

VL - 28

SP - 1833

EP - 1849

JO - Soft Computing

JF - Soft Computing

IS - 3

ER -

(⊙ , ∨) -Derivations on MV-algebras

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