On submodule transitivity of QTAG-modules
In this paper, we generalize a suitable transformation from an element-based to a submodule-based interpretation of the traditional idea of transitivity in QTAG modules. We examine QTAG modules that are transitive in the sense that the module has an automorphism that sends one isotype submodule $ K...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-02-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023467?viewType=HTML |
| _version_ | 1827999923482656768 |
|---|---|
| author | Fahad Sikander Firdhousi Begam Tanveer Fatima |
| author_facet | Fahad Sikander Firdhousi Begam Tanveer Fatima |
| author_sort | Fahad Sikander |
| collection | DOAJ |
| description | In this paper, we generalize a suitable transformation from an element-based to a submodule-based interpretation of the traditional idea of transitivity in QTAG modules. We examine QTAG modules that are transitive in the sense that the module has an automorphism that sends one isotype submodule $ K $ onto any other isotype submodule $ K' $, unless this is impossible because either the submodules or the quotient modules are not isomorphic. Additionally, the classes of strongly transitive and strongly $ U $-transitive QTAG modules are defined using a slight adaptations of this. This work investigates the latter class in depth, demonstrating that every $ \alpha $- module is strongly transitive with regard to countably generated isotype submodules. |
| first_indexed | 2024-04-10T06:06:07Z |
| format | Article |
| id | doaj.art-5c04f220935645e0b5547c7940a49b71 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T06:06:07Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-5c04f220935645e0b5547c7940a49b712023-03-03T01:23:16ZengAIMS PressAIMS Mathematics2473-69882023-02-01849303931310.3934/math.2023467On submodule transitivity of QTAG-modulesFahad Sikander0Firdhousi Begam1Tanveer Fatima21. Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Jeddah 23442, Saudi Arabia2. Applied Science Section, University Polytechnic, Aligarh Muslim University, Aligarh 202002, Uttar Pradesh, India3. Department of Mathematics and Statistics, College of Sciences, Taibah University, Yanbu 41911, Saudi ArabiaIn this paper, we generalize a suitable transformation from an element-based to a submodule-based interpretation of the traditional idea of transitivity in QTAG modules. We examine QTAG modules that are transitive in the sense that the module has an automorphism that sends one isotype submodule $ K $ onto any other isotype submodule $ K' $, unless this is impossible because either the submodules or the quotient modules are not isomorphic. Additionally, the classes of strongly transitive and strongly $ U $-transitive QTAG modules are defined using a slight adaptations of this. This work investigates the latter class in depth, demonstrating that every $ \alpha $- module is strongly transitive with regard to countably generated isotype submodules. https://www.aimspress.com/article/doi/10.3934/math.2023467?viewType=HTMLqtag modulesnice submodulestotally projective moduleisotype submoduleulm-kaplansky invariants |
| spellingShingle | Fahad Sikander Firdhousi Begam Tanveer Fatima On submodule transitivity of QTAG-modules AIMS Mathematics qtag modules nice submodules totally projective module isotype submodule ulm-kaplansky invariants |
| title | On submodule transitivity of QTAG-modules |
| title_full | On submodule transitivity of QTAG-modules |
| title_fullStr | On submodule transitivity of QTAG-modules |
| title_full_unstemmed | On submodule transitivity of QTAG-modules |
| title_short | On submodule transitivity of QTAG-modules |
| title_sort | on submodule transitivity of qtag modules |
| topic | qtag modules nice submodules totally projective module isotype submodule ulm-kaplansky invariants |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023467?viewType=HTML |
| work_keys_str_mv | AT fahadsikander onsubmoduletransitivityofqtagmodules AT firdhousibegam onsubmoduletransitivityofqtagmodules AT tanveerfatima onsubmoduletransitivityofqtagmodules |