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On (f, g)-derivations of lattice implication algebras

김경호
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2021.08|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제22권 제1호|pp. 55-63|DOI 10.30948/afmi.2021.22.1.55

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참고문헌

키워드

Lattice implication algebra$(fg)$-derivationnormal filter$D$-normal filter$Fix_D(L)$ $Ker D$

초록

In this paper, we introduce the notion of $(f, g)$-derivation of lattice implication algebra and investigated some related properties. Also, we prove that if $D$ is an $(f, g)$-derivation on $L$ and $f(x)\le g(x)$ for every $x\in L,$ then we get $D(x\to y)=f(x)\to D(y)$ for all $x, y\in L$.

Abstract

In this paper, we introduce the notion of $(f, g)$-derivation of lattice implication algebra and investigated some related properties. Also, we prove that if $D$ is an $(f, g)$-derivation on $L$ and $f(x)\le g(x)$ for every $x\in L,$ then we get $D(x\to y)=f(x)\to D(y)$ for all $x, y\in L$.

참고문헌 (5)

  1. Y. Xu, "Lattice implication algebras", J. Southwest Jiaotong Univ, 1, pp.20~27 (1993)
  2. Y. Xu, "Lattice H implication algebras and lattice implication algebra classes", J. Hebei Mining and Civil Engineering Institute, 3, pp.139~143 (1992)
  3. Y. Xu, "On filters of lattice implication algebras", J. Fuzzy Math, 1(2), pp.251~260 (1993)
  4. S. D. Lee, "On derivations of lattice implication algebras", Ars Combinatoria, 27(4), pp.1119~1131 (2019)
  5. Y. H. Yon, "On f-derivations of lattice implication algebras", Ars Combinatoria, 110, pp.205~215 (2013)

관련 논문AI추천

On generalized $f$-derivations of lattice implication algebras김경호강원경기수학회 · 한국수학논문집2019 · 제27권 제4호On generalized derivations of lattice implication algebras김경호기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2020 · 제20권 제2호On Symmetric Bi-$f$-derivations of Lattice Implication Algebras김경호영남수학회 · East Asian Mathematical Journal2020 · 제36권 제1호ON f-DERIVATIONS OF LATTICESMehmet Ali Ozturk, Yılmaz Ceven대한수학회 · 대한수학회보2008 · 제45권 제4호Derivations on subtraction algebrasMehmet Ali Öztürk, Yilmaz Ceven대한수학회 · 대한수학회논문집2009 · 제24권 제4호ON f-DERIVATIONS FROM SEMILATTICES TO LATTICES김경호, 연용호대한수학회 · 대한수학회논문집2014 · 제29권 제1호

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