بررسی مدول های α- کوتاه موازی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه ریاضی، دانشکده علوم، دانشگاه تربیت دبیر شهید رجایی، تهران، ایران

2 گروه ریاضی، دانشکده علوم ریاضی و کامپیوتر، دانشگاه شهید چمران اهواز، اهواز، ایران

چکیده

در اﯾﻦ ﻣﻘﺎﻟﻪ ﻣﺪولﻫﺎی α-ﮐﻮﺗﺎه ﻣﻮازی را ﺗﻌﺮﯾﻒ ﻣﯽﮐﻨﯿﻢ و وﯾﮋﮔﯽﻫﺎی اﺳﺎﺳﯽ ﻣﺪولﻫﺎی ﮐﻮﺗﺎه

را ﺑﺮای ﻣﺪولﻫﺎی α-ﮐﻮﺗﺎه ﻣﻮازی ﺗﻌﻤﯿﻢ ﻣﯽدﻫﯿﻢ. ﻫﻤﭽﻨﯿﻦ ارﺗﺒﺎط وﯾﮋﮔﯽ α-ﮐﻮﺗﺎه ﻣﻮازی ﺑﺎ ﺑﻌﺪ ﻧﻮﯾﺘﺮی

ﻣﻮازی ﻣﺪول را ﺑﺮرﺳﯽ ﻣﯽﮐﻨﯿﻢ و ﻧﺸﺎن ﻣﯽدﻫﯿﻢ ﮐﻪ اﮔﺮ M ﯾﮏ ﻣﺪول α-ﮐﻮﺗﺎه ﻣﻮازی ﺑﺎﺷﺪ، آنﮔﺎه

M دارای ﺑﻌﺪ ﻧﻮﯾﺘﺮی ﻣﻮازی اﺳﺖ و ١ + α ⩽ n-dim M ⩽ α. ﺑﻪ وﯾﮋه ﻧﺘﯿﺠﻪ ﻣﯽ ﮔﯿﺮﯾﻢ ﮐﻪ

ﮐﻪ اﮔﺮ M ﯾﮏ ﻣﺪول α-ﮐﻮﺗﺎه ﻣﻮازی ﺑﺎ ﺑﻌﺪ ﮔﻠﺪی ﻣﺘﻨﺎﻫﯽ ﺑﺎﺷﺪ، آنﮔﺎه M دارای ﺑﻌﺪ ﻧﻮﯾﺘﺮی اﺳﺖ و

α ≤ n-dimM ≤ α + ١.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

On $\alpha$-parallel short modules

نویسندگان [English]

  • Sayed Malek Javdannezhad 1
  • nasrin shirali 2
  • Maryam shirali 2
  • Sayedeh Fatemah Mousavinasab 2
1 Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
2 ِDepartment of Mathematics, Faculty of Mathematics and Computer Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran
چکیده [English]

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 ordinal

number with this property. Using this concept, we extend some of the basic results of $\alpha$-short modules

to $\alpha$-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 short

module with finite Goldie dimension, then $M$ has Noetherian dimension and $\alpha\leq\ndim\, M\leq\alpha+1$.

کلیدواژه‌ها [English]

  • parallel Noetherian dimension
  • $\alpha$-parallel short modules
  • $\alpha$-parallel atomic modules
  • $\alpha$-almost parallel Noetherian modules
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