The semisimple dimension of a certain type of module
In this paper we define and study a new kind of dimension called, semisimple dimension, that measures how far a module is from being semisimple. Like other kinds of dimensions, this is an ordinal valued invariant. It is shown that a Noetherian module with semisimple dimension is an Artinian module....
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| Date: | 2026 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2026
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2354 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1861680840591802368 |
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| author | Tognon, Carlos Henrique |
| author_facet | Tognon, Carlos Henrique |
| author_sort | Tognon, Carlos Henrique |
| baseUrl_str | https://admjournal.luguniv.edu.ua/index.php/adm/oai |
| collection | OJS |
| datestamp_date | 2026-04-05T09:02:49Z |
| description | In this paper we define and study a new kind of dimension called, semisimple dimension, that measures how far a module is from being semisimple. Like other kinds of dimensions, this is an ordinal valued invariant. It is shown that a Noetherian module with semisimple dimension is an Artinian module. Moreover, we involve the theory of graphs within of such dimension achieving some applications for the edge ideal of a graph. |
| doi_str_mv | 10.12958/adm2354 |
| first_indexed | 2026-04-06T01:00:02Z |
| format | Article |
| id | admjournalluguniveduua-article-2354 |
| institution | Algebra and Discrete Mathematics |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-04-06T01:00:02Z |
| publishDate | 2026 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-23542026-04-05T09:02:49Z The semisimple dimension of a certain type of module Tognon, Carlos Henrique uniform dimension, semisimple module, Artinian module, edge ideal of a graph 13C13 In this paper we define and study a new kind of dimension called, semisimple dimension, that measures how far a module is from being semisimple. Like other kinds of dimensions, this is an ordinal valued invariant. It is shown that a Noetherian module with semisimple dimension is an Artinian module. Moreover, we involve the theory of graphs within of such dimension achieving some applications for the edge ideal of a graph. Lugansk National Taras Shevchenko University 2026-04-05 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2354 10.12958/adm2354 Algebra and Discrete Mathematics; Vol 41, No 1 (2026) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2354/pdf Copyright (c) 2026 Algebra and Discrete Mathematics |
| spellingShingle | uniform dimension semisimple module Artinian module edge ideal of a graph 13C13 Tognon, Carlos Henrique The semisimple dimension of a certain type of module |
| title | The semisimple dimension of a certain type of module |
| title_full | The semisimple dimension of a certain type of module |
| title_fullStr | The semisimple dimension of a certain type of module |
| title_full_unstemmed | The semisimple dimension of a certain type of module |
| title_short | The semisimple dimension of a certain type of module |
| title_sort | semisimple dimension of a certain type of module |
| topic | uniform dimension semisimple module Artinian module edge ideal of a graph 13C13 |
| topic_facet | uniform dimension semisimple module Artinian module edge ideal of a graph 13C13 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2354 |
| work_keys_str_mv | AT tognoncarloshenrique thesemisimpledimensionofacertaintypeofmodule AT tognoncarloshenrique semisimpledimensionofacertaintypeofmodule |