| Title:
|
Eventually semisimple weak $FI$-extending modules (English) |
| Author:
|
Takıl Mutlu, Figen |
| Author:
|
Tercan, Adnan |
| Author:
|
Yaşar, Ramazan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
148 |
| Issue:
|
2 |
| Year:
|
2023 |
| Pages:
|
211-222 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article, we study modules with the weak $FI$-extending property. We prove that if $M$ satisfies weak $FI$-extending, pseudo duo, $C_3$ properties and $M/{\rm Soc} M$ has finite uniform dimension then $M$ decomposes into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if $M$ satisfies the weak $FI$-extending, pseudo duo, $C_3$ properties and ascending (or descending) chain condition on essential submodules then $M=M_1\oplus M_2$ for some semisimple submodule $M_1$ and Noetherian (or Artinian, respectively) submodule $M_2$. Moreover, we show that a nonsingular weak $CS$ (or weak $C_{11}^*$, or weak $FI$) module has a direct summand which essentially contains the socle of the module and is a $CS$ (or $C_{11}$, or $FI$-extending, respectively) module. (English) |
| Keyword:
|
$CS$-module |
| Keyword:
|
weak $CS$-module |
| Keyword:
|
uniform dimension |
| Keyword:
|
ascending chain on essential submodules |
| Keyword:
|
$C_{11}$-module |
| Keyword:
|
$FI$-extending |
| Keyword:
|
weak $FI$-extending |
| MSC:
|
16D50 |
| MSC:
|
16D80 |
| idZBL:
|
Zbl 07729573 |
| idMR:
|
MR4585577 |
| DOI:
|
10.21136/MB.2022.0100-21 |
| . |
| Date available:
|
2023-05-04T17:57:46Z |
| Last updated:
|
2023-09-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151685 |
| . |
| Reference:
|
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