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| Summary: | 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. |
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| DOI: | 10.12958/adm2354 |