TY - JOUR
ID - 19540
TI - α-TYPE SHORT MODULES
JO - مجله مدلسازی پیشرفته ریاضی
JA - JAMM
LA - fa
SN - 2251-8088
AU - Shirali, Nasrin
AU - Javdannezhad, Sayed Malek
AU - Kavoosi Ghafi, Hooriy
AD - ِDepartment of mathematics shahid chamran university of ahvaz , ahvaz iran
AD - Shahid Rajaee Teacher Training University,
Y1 - 2024
PY - 2024
VL - 14
IS - (English)3
SP - 41
EP - 53
KW - type Noetherian dimension
KW - $\alpha$-type atomic modules
KW - $\alpha$-type short modules
KW - $\alpha$-almost type Noetherian modules
DO - 10.22055/jamm.2024.47531.2296
N2 - 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 $\tndim\, (M)=\alpha+1$.
UR - https://jamm.scu.ac.ir/article_19540.html
L1 - https://jamm.scu.ac.ir/article_19540_194c7317a13a3b0aae82f67d2528cfcd.pdf
ER -