@article {
author = {Shirali, Nasrin and Javdannezhad, Sayed Malek and Kavoosi Ghafi, Hooriy},
title = {α-TYPE SHORT MODULES},
journal = {Journal of Advanced Mathematical Modeling},
volume = {14},
number = {(English)3},
pages = {41-53},
year = {2024},
publisher = {Shahid Chamran University of Ahvaz},
issn = {2251-8088},
eissn = {2645-6141},
doi = {10.22055/jamm.2024.47531.2296},
abstract = {In this paper, we first consider the concept of type Noetherian dimension of a module such as $M$, which is dual of the type Krull dimension, denoted by $\tndim\, (M)$, and defined to be the codeviation of the poset of the type submodules of $M$, then we dualize some basic results of type Krull dimension for type Noetherian dimension. In the following, we introduce the concept of $\alpha$-type short modules (i.e., for each type submodule $A$ of $M$, either $\ndim\, (\frac{M}{A})\leq \alpha$ or $\tndim\, (A)\leq \alpha$ and $\alpha$ is the least ordinal number with this property), and extend some basic results of $\alpha$-short modules to $\alpha$-type short modules. In particular, it is proved that if $M$ is an $\alpha$-type short module, then it has type Noetherian dimension and $\tndim\, (M)=\alpha$ or $\tndim\, (M)=\alpha+1$.},
keywords = {type Noetherian dimension,$\alpha$-type atomic modules,$\alpha$-type short modules,$\alpha$-almost type Noetherian modules},
title_fa = {α-TYPE SHORT MODULES},
abstract_fa = {In this paper, we first consider the concept of type Noetherian dimension of a module such as $M$, which is dual of the type Krull dimension, denoted by $\tndim\, (M)$, and defined to be the codeviation of the poset of the type submodules of $M$, then we dualize some basic results of type Krull dimension for type Noetherian dimension. In the following, we introduce the concept of $\alpha$-type short modules (i.e., for each type submodule $A$ of $M$, either $\ndim\, (\frac{M}{A})\leq \alpha$ or $\tndim\, (A)\leq \alpha$ and $\alpha$ is the least ordinal number with this property), and extend some basic results of $\alpha$-short modules to $\alpha$-type short modules. In particular, it is proved that if $M$ is an $\alpha$-type short module, then it has type Noetherian dimension and $\tndim\, (M)=\alpha$ or $\tndim\, (M)=\alpha+1$.},
keywords_fa = {type Noetherian dimension,$\alpha$-type atomic modules,$\alpha$-type short modules,$\alpha$-almost type Noetherian modules},
url = {https://jamm.scu.ac.ir/article_19540.html},
eprint = {https://jamm.scu.ac.ir/article_19540_194c7317a13a3b0aae82f67d2528cfcd.pdf}
}