In this article we introduce and study the concept of α-almost Artinian modules. We show that each α-almost Artinian module M is almost Artinian (i.e., every proper homomorphic image of M is Artinian), where α ∈ {0,1}. Using this concept we extend some of the basic results of almost Artinian modules to α-almost Artinian modules. Moreover we introduce and study the concept of α-Krull modules. We observe that if M is an α-Krull module then the Krull dimension of M is either α or α + 1.
@article{bwmeta1.element.doi-10_1515_math-2016-0036,
author = {Maryam Davoudian and Ahmad Halali and Nasrin Shirali},
title = {On$\alpha$-almost Artinian modules},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {404-413},
zbl = {06632369},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0036}
}
Maryam Davoudian; Ahmad Halali; Nasrin Shirali. Onα-almost Artinian modules. Open Mathematics, Tome 14 (2016) pp. 404-413. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0036/