@article{Alotaibi2026, 
author = {Nura Alotaibi},
title = {On Jordan    σ-centralizers and related linear maps in algebras},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {4571-4585},
keywords = {Jordan σ-centralizers, zero-product, algebras isomorphism, generalized matrix algebras, upper-triangular algebras, von Neumann algebras, standard operator algebras, nest algebras},
url = {https://www.sciopen.com/article/10.3934/math.2026184},
doi = {10.3934/math.2026184},
abstract = {Let        B   be an algebra over a commutative ring with identity    S, and let    σ:        B    →      B   be an algebra homomorphism. In this paper, we study linear operators    Δ:        B    →      B   that are constrained by zero-product conditions involving the Jordan product    u  ∘  v  =  u  v  +  v  u. In particular, we consider mappings that satisfy     u  v  =  0  ⇒  Δ  (  u  ∘  v  )  =  Δ  (  u  )  ∘  σ  (  v  )  ,        u  v  =  0  ⇒  Δ  (  u  ∘  v  )  =  σ  (  u  )  ∘  Δ  (  v  )  ,and     u  v  =  0  ⇒  Δ  (  u  ∘  v  )  =  Δ  (  u  )  ∘  σ  (  v  )  =  σ  (  u  )  ∘  Δ  (  v  )  .Assuming the endomorphism    σ is bijective, we prove that the scenario essentially simplifies to the identity case    σ  =            i      d                      B            . Such a simplification enables a comprehensive the forms of these linear operators. As a result, we obtain precise expressions for these operators across diverse algebraic structures, including generalized matrix algebras, upper-triangular algebras, von Neumann algebras, standard operator algebras, and nest algebras. Moreover, this approach produces analogous results for Jordan    σ-centralizers, thus extending and integrating various prior findings in the field.}
}