@article{Al-Mallah2026, 
author = {Omar Al-Mallah and Mohammed Abu-Saleem and Noômen Jarboui},
title = {On idempotent-fine group rings},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {345-352},
keywords = {group ring, fine ring, idempotent-fine ring},
url = {https://www.sciopen.com/article/10.3934/math.2026014},
doi = {10.3934/math.2026014},
abstract = {Let    A be an associative ring. A nonzero element    t  ∈  A is called fine if it can be written as    t  =  n  +  v, where    v is a unit and    n is a nilpotent element. A ring    A is called an idempotent-fine ring if every nonzero idempotent in    A is fine. Let    A be a ring (respectively, an integral domain) of characteristic        p    m   for some prime    p and positive integer    m, and let    G be a locally finite nilpotent group (respectively, a locally finite group). We proved that    A  [  G  ] is an idempotent-fine ring if and only if    G is a    p-group. Moreover, if    F is a field of characteristic    p and    F  [  G  ] is an idempotent-fine ring, then every nontrivial element    g in the group    G of finite order is a    p-element. Conversely, if G is a locally finite    p-group, then    F  [  G  ] is an idempotent-fine ring.}
}