On generalized derivations of partially ordered sets

Abdelwanis, Ahmed Y.; Boua, Abdelkarim

doi:10.2478/cm-2019-0006

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2022

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“…The notion of (∧, ∨)-derivation on a lattice is witnessing increased attention. It studies, among others, in partially ordered sets [1,31], in distributive lattices [30], in semilattices [29], in bounded hyperlattices [24], in quantales and residuated lattices [10,25] and in several kinds of algebras [14,17,19]. Furthermore, it used in the definition of congruences and ideals in a distributive lattice [20].…”

Section: Introductionmentioning

confidence: 99%

(F,G)-Derivations on a Lattice

AMROUNE¹,

ZEDAM²,

YETTOU³

2022

KgJMat

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In the present paper, we introduce the notion of (F,G)-derivation on a lattice as a generalization of the notion of (∧,∨)-derivation. This newly notion is based on two arbitrary binary operations F and G instead of the meet (∧) and the join (∨) operations. Also, we investigate properties of (F,G)-derivation on a lattice in details. Furthermore, we deﬁne and study the notion of principal (F,G)-derivations as a particular class of (F,G)-derivations. As applications, we provide two representations of a given lattice in terms of its principal (F,G)-derivations.

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