%0 Journal Article
%T On $\alpha$-parallel short modules
%J Journal of Advanced Mathematical Modeling
%I Shahid Chamran University of Ahvaz
%Z 2251-8088
%A Javdannezhad, Sayed Malek
%A shirali, nasrin
%A shirali, Maryam
%A Mousavinasab, Sayedeh Fatemah
%D 2022
%\ 09/23/2022
%V 12
%N 3
%P 437-447
%! On $\alpha$-parallel short modules
%K parallel Noetherian dimension
%K $\alpha$-parallel short modules
%K $\alpha$-parallel atomic modules
%K $\alpha$-almost parallel Noetherian modules
%R 10.22055/jamm.2022.41194.2053
%X An $R$-module $M$ is called $\alpha$-parallel short modules, if for each parallel submodule $N$ to $M$ either $\pndim\, N \leq \alpha$ or $\ndim\, \frac{M}{N}\leq\alpha$ and $\alpha$ is the least ordinalnumber with this property. Using this concept, we extend some of the basic results of $\alpha$-short modulesto $\alpha$-parallel short modules.Also, we have studied the relationship between $\alpha$-parallel short modules and their parallel Noetherian dimension and we show that if $M$ is a $\alpha$-parallel short module, then $M$ has parallel Noetherian dimension and$\alpha\leq\pndim\, M\leq \alpha+1$. Furthermore, we prove that if $M$ is an $\alpha$-parallel shortmodule with finite Goldie dimension, then $M$ has Noetherian dimension and $\alpha\leq\ndim\, M\leq\alpha+1$.
%U https://jamm.scu.ac.ir/article_17876_fd16aa91922dd3d46065234f5c5cc928.pdf