Ring and module theory: To the connection between C1 and a modified form of C1 and to the significance of C2 and semi-I-regularity for exchange properties
- I introduce a stronger version of CS-modules which lies between CS- and quasi-continuous modules. Moreover I analyze modules with the property C2 that are not necessarily continuous or auto-invariant. Here some results also hold for large restricted modules, which is a weaker property compared to C2. Finally I introduce the definition of semi-I-regular modules as a generalization of the definition of semiregular modules and show that every semi-I-regular module has the finite exchange property and even the exchange property if it further is a module with LE-decomposition or a Utumi module.
| Author: | Alexander BlankGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1284322 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/128432 |
| Advisor: | Wolfgang SchneiderGND |
| Type: | Doctoral Thesis |
| Language: | English |
| Date of Publication (online): | 2026/02/28 |
| Year of first Publication: | 2026 |
| Publishing Institution: | Universität Augsburg |
| Granting Institution: | Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Date of final exam: | 2025/12/17 |
| Release Date: | 2026/03/24 |
| Tag: | Continuous Modules; Utumi modules; clean modules; exchange property; semiregular module |
| GND-Keyword: | Modultheorie; Stetiger Modul |
| Page Number: | 75 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Algebra und Zahlentheorie | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY-NC 4.0: Creative Commons: Namensnennung - Nicht kommerziell |
