On submodule transitivity of QTAG-modules
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| Názov: | On submodule transitivity of QTAG-modules |
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| Autori: | Fahad Sikander, Firdhousi Begam, Tanveer Fatima |
| Zdroj: | AIMS Mathematics, Vol 8, Iss 4, Pp 9303-9313 (2023) |
| Informácie o vydavateľovi: | American Institute of Mathematical Sciences (AIMS), 2023. |
| Rok vydania: | 2023 |
| Predmety: | Monoclonal antibody, Artificial intelligence, Class (philosophy), Study of properties and structures of commutative rings, FOS: Political science, Immunology, Cluster Algebras and Triangulated Categories, FOS: Law, isotype submodule, Biochemistry, Gene, 01 natural sciences, Fuzzy Logic and Residuated Lattices, QA1-939, FOS: Mathematics, Genetics, 0101 mathematics, Biology, Political science, Antibody, Algebra and Number Theory, FOS: Clinical medicine, ulm-kaplansky invariants, Pure mathematics, nice submodules, Discrete mathematics, 16. Peace & justice, Automorphism, Computer science, qtag modules, Chemistry, Computational Theory and Mathematics, Quotient, totally projective module, Combinatorics, FOS: Biological sciences, Physical Sciences, Computer Science, Transformation (genetics), Element (criminal law), Geometry and Topology, Modal Logics, Transitive relation, Law, Mathematics, Isotype, Sequence (biology) |
| Popis: | 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. |
| Druh dokumentu: | Article Other literature type |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2023467 |
| DOI: | 10.60692/ahsgs-5ph88 |
| DOI: | 10.60692/8djbe-ssw94 |
| Prístupová URL adresa: | https://doaj.org/article/5c04f220935645e0b5547c7940a49b71 |
| Prístupové číslo: | edsair.doi.dedup.....97e280f934cd5cd228dc143586664eb0 |
| Databáza: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | 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. |
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| ISSN: | 24736988 |
| DOI: | 10.3934/math.2023467 |