A NEW STUDY OF GENERALIZED  $\theta$--DERIVATION INVOLVING MAPPINGS  IN LATTICES

Aftab Ahmed Aftab; Mukhtar Ahmad; Muhammad Saleem; Muhammad Asif Javed; Muhammad Danial Faiz; Ather Qayyum

doi:10.5269/bspm.77829

Aftab Ahmed Aftab Department of Mathematics, University of Southern Punjab Multan, Pakistan
Mukhtar Ahmad Department of Mathematics, Khawaja Fareed University of Engineering and Information Technology Rahim Yar Khan, Pakistan
Muhammad Saleem National College of Business Administration and Economics Multan Campus, Pakistan
Muhammad Asif Javed Department of Mathematics, University of Southern Punjab Multan, Pakistan.
Muhammad Danial Faiz Department of Mathematics, University of Southern Punjab Multan, Pakistan.
Ather Qayyum Department of Mathematics, University of Southern Punjab Multan, Pakistan.

Abstract

The primary objective of this study is to explore and establish significant structural properties of lattices in the context of $\theta$-generalized derivations. We investigate the interplay between mappings and the intrinsic order structure of lattices, with particular emphasis on functions and their associated mappings. A central focus is the development and representation of $\theta$-generalized derivations involving left centralizers. Furthermore, we rigorously analyze and prove several fundamental results that elucidate the behavior and characteristics of these derivations within lattice frameworks. This work contributes to a deeper understanding of algebraic structures governed by generalized derivations and their functional mappings in ordered systems.

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