@Article{CMR-34-1,
author = {Ouyang, Lunqun and Zhou, Qiong and Liu, Jinwang and Yueming, Xiang},
title = {Extensions of Modules with ACC on $d$-Annihilators},
journal = {Communications in Mathematical Research },
year = {2018},
volume = {34},
number = {1},
pages = {23--35},
abstract = {<p style="text-align: justify;">A unitary right $R$-module $M_R$ satisfies acc on $d$-annihilators if for every sequence $(a_n)_n$ of elements of $R$ the ascending chain ${\rm Ann}_M(a_1)\subseteq{\rm Ann}_M(a_1a_2)\subseteq{\rm Ann}_M(a_1a_2a_3)\subseteq\cdots$ of submodules of $M_R$ stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on $d$-annihilators. Then we show that under some additional conditions, the Ore extension module $M[x]_{R[x;\alpha,\delta]}$ over the Ore extension ring $R[x;\,\alpha,\delta]$ satisfies acc on $d$-annihilators if and only if the module $M_R$ satisfies acc on $d$-annihilators. Consequently, several known results regarding&nbsp; modules with acc on $d$-annihilators are extended to a more general setting.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.13447/j.1674-5647.2018.01.03},
url = {https://global-sci.com/article/81581/extensions-of-modules-with-acc-on-d-annihilators}
}