Structural Properties of (l,r)- and (r, l)-Derivations in IUP-Algebras

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DOI: https://doi.org/10.28924/2291-8639-23-2025-334
Published: Dec 12, 2025
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Nalinthip Phaeyai, Chanchanok Langsun, Aphinya Thongkham, Aiyared Iampan, Structural Properties of (l,r)- and (r, l)-Derivations in IUP-Algebras, Int. J. Anal. Appl., 23 (2025), 334.

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Nalinthip Phaeyai, Chanchanok Langsun, Aphinya Thongkham, Aiyared Iampan

Abstract

The notion of derivations in BCI-algebras was initially introduced by Jun and Xin in 2004 [18], providing a foundation for structural analysis in non-classical logics. In this paper, we extend the study of derivations to the framework of IUP-algebras X = (X, ·, 0) by introducing and examining two new types: (l,r)-derivations and (r, l)- derivations. These operators are defined via the binary operation ∧ given by x∧y = (y · x)· x for all x, y ∈ X, which plays a central role in the algebraic structure. We explore fundamental properties of these derivations, analyze their interaction with IUP-substructures, and establish several characterizations. Additionally, we define two special subsets—Kerd(X) (the kernel) and Fixd(X) (the fixed-point set)—associated with a derivation d, and investigate conditions under which they exhibit algebraic regularity. Our results enrich the theory of derivations in IUP-algebras and open new directions for the study of morphism-based operations in non-associative systems.

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