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$(φ, ψ)$ $(φ, ψ)$ -derivations of BL-algebras

S. Alsatayhi

Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran

E-mail Address: a.sawsan@modares.ac.ir

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and

A. Moussavi

Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran

E-mail Address: moussavi.a@modares.ac.ir

Corresponding author.

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https://doi.org/10.1142/S179355711850016XCited by:2 (Source: Crossref)

Abstract

In this paper, the notions of derivations of types $1$ $1$ and $2$ $2$ on a BL-algebra $L$ $L$ are introduced. We extend the notions of these derivations by introducing the notions of $(φ, ψ)$ $(φ, ψ)$ -derivations of types $1$ $1$ and $2$ $2$ , and discuss some related properties. The conditions for $(φ, ψ)$ $(φ, ψ)$ -derivations of types $1$ $1$ and $2$ $2$ to be isotone are provided. The set ${Fix}_{D} (L)$ ${Fix}_{D} (L)$ is defined and conditions for ${Fix}_{D} (L)$ ${Fix}_{D} (L)$ to be a down closed set and an ideal on $L$ $L$ are given where $L$ $L$ is a Boolean algebra and $D$ $D$ is a $(φ, ψ)$ $(φ, ψ)$ -derivation of type $1$ $1$ on $L$ $L$ . Finally, the relationship between $φ$ $φ$ -derivations of types $1$ $1$ and $2$ $2$ for a Boolean algebra $L$ $L$ is determined.

Communicated by P. Corsini

Keywords:

AMSC: 06D35, 03G05, 13N15

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