@article{Luo2026, 
author = {Yingyu Luo and Qian Chen},
title = {Identities with inverses on matrix rings over a division ring of characteristic two},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {3},
pages = {5283-5298},
keywords = {identities with inverses on rings, derivation, matrix ring, division ring},
url = {https://www.sciopen.com/article/10.3934/math.2026217},
doi = {10.3934/math.2026217},
abstract = {Let        D   be a division ring with char   (      D    )  =  2. Let        R    =      M    n    (      D    ) be the ring of all    n  ×  n matrices over        D  , where    n  ≥  2. Let    f  ,  g  :      R    →      R   be two additive maps such that     f  (  A  )  +  A  g  (      A          −      1        )  A  =  0for all invertible    A  ∈      R  . If        |        D        |    ≠  2  ,  4  ,  8, then     f  (  A  )  =  A  Q  +  δ  (  A  )    and    g  (  A  )  =  Q  A  +  δ  (  A  )for all invertible    A  ∈      R  , where    A  ∈      R   and    δ is a derivation of        R  . This result affirmatively answers a question posed by Argac et al. under a mild condition.}
}