(⊙,∨)-Derivations on MV-algebras

被引：0
|
作者：
Zhao, Xueting [1 ]
Gan, Aiping [2 ]
Yang, Yichuan [1 ]
机构：
[1] Beihang Univ, Sch Math Sci, Shahe Campus, Beijing 102206, Peoples R China
[2] Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Peoples R China
来源：
SOFT COMPUTING | 2024年 / 28卷 / 03期
关键词：
MV-algebra; Derivation; Direct product; Complete lattice; Boolean center; Ideal; Fixed point set; DERIVATIONS;
D O I：
10.1007/s00500-023-09384-2
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
Let A be an MV-algebra. An (circle dot,boolean OR)-derivation on A is a map d : A -> A satisfying: d(x circle dot y) = (d(x) circle dot y) boolean OR (x circle dot d(y)) for all x, y is an element of A. This paper initiates the study of (circle dot,boolean OR)-derivations on MV-algebras. Several families of (circle dot,boolean OR)-derivations on an MV-algebra are explicitly constructed to give realizations of the underlying lattice of an MV-algebra as lattices of (circle dot,boolean OR)-derivations. Furthermore, (circle dot,boolean OR)-derivations on a finite MV-chain are enumerated and the underlying lattice is described.
引用
收藏
页码：1833 / 1849
页数：17
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