@article{Raza2024, 
author = {Mohd Arif Raza and Huda Eid Almehmadi},
title = {Lie (Jordan)  σ−centralizer at the zero products on generalized matrix algebra},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {26631-26648},
keywords = {generalized matrix algebra, Lie (Jordan) σ−centralizer, σ−centralizer},
url = {https://www.sciopen.com/article/10.3934/math.20241295},
doi = {10.3934/math.20241295},
abstract = {Given a unital commutative ring  R,  (A,B) and  (B,A) are bimodules of  M and  N, respectively, where  A,B are unitals  R−algebras. The  R−algebra  G=  G(A,M,N,B) is a generalized matrix algebra described by the Morita context  (A,B,M,N,ζMN,χNM). The present study investigated the structure of Lie (Jordan)  σ−centralizers at the zero products on order two generalized matrix algebra and established that each Jordan  σ−centralizer at the zero products is a  σ−centralizer at the zero product on order two generalized matrix algebra. We also provided sufficient and necessary conditions under which a Lie  σ−centralizer at the zero product is proper on an order two generalized matrix algebra.}
}