TY - JOUR
ID - 17876
TI - On $\alpha$-parallel short modules
JO - Journal of Advanced Mathematical Modeling
JA - JAMM
LA - en
SN - 2251-8088
AU - Javdannezhad, Sayed Malek
AU - shirali, nasrin
AU - shirali, Maryam
AU - Mousavinasab, Sayedeh Fatemah
AD - Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
AD - ِDepartment of Mathematics, Faculty of Mathematics and Computer Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Y1 - 2022
PY - 2022
VL - 12
IS - 3
SP - 437
EP - 447
KW - parallel Noetherian dimension
KW - $\alpha$-parallel short modules
KW - $\alpha$-parallel atomic modules
KW - $\alpha$-almost parallel Noetherian modules
DO - 10.22055/jamm.2022.41194.2053
N2 - 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 $\alpha\leq\ndim\, M\leq\alpha+1$.
UR - https://jamm.scu.ac.ir/article_17876.html
L1 - https://jamm.scu.ac.ir/article_17876_fd16aa91922dd3d46065234f5c5cc928.pdf
ER -