@article{Jun2025, 
author = {Young Bae Jun and Ravikumar Bandaru and Amal S. Alali},
title = {Endomorphic GE-derivations},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {1792-1813},
keywords = {Kernel, Ω(l, r)-endomorphic GE-derivation, Ω(r, l)-endomorphic GE-derivation, Endomorphism, GE-filter},
url = {https://www.sciopen.com/article/10.3934/math.2025082},
doi = {10.3934/math.2025082},
abstract = {Using the binary operation "       ↰  " on a GE-algebra        X   given by        ↰    (      x    ,      y    )  =  (      y        ∗        x    )      ∗        x   and the GE-endomorphism        Ω    :      X    →      X  , the notion of              Ω              (      l      ,      r      )      -endomorphic (resp.,              Ω              (      r      ,      l      )      -endomorphic) GE-derivation is introduced, and several properties are investigated. Also, examples that illustrate these are provided. Conditions under which              Ω              (      l      ,      r      )      -endomorphic GE-derivations or              Ω              (      l      ,      r      )      -endomorphic GE-derivations to satisfy certain equalities and inequalities are studied. We explored the conditions under which        f   becomes order preserving when        f   is an              Ω              (      l      ,      r      )      -endomorphic GE-derivation or an              Ω              (      r      ,      l      )      -endomorphic GE-derivation on        X  . The        f  -kernel and        Ω  -kernel of        f   formed by the              Ω              (      r      ,      l      )      -endomorphic GE-derivation or              Ω              (      l      ,      r      )      -endomorphic GE-derivation turns out to be GE-subalgebras. It is observed that the        Ω  -kernel of        f   is a GE-filter of        X  . The condition under which the        f  -kernel of        f   formed by the              Ω              (      r      ,      l      )      -endomorphic GE-derivation or              Ω              (      l      ,      r      )      -endomorphic GE-derivation becomes a GE-filter is explored.}
}