Title: Generalized injectivity and approximations Author: Serap S¸ahinkaya Department:Algebra Faculty of Mathematics and Physics, Charles University Supervisor: Prof. RNDr. Jan Trlifaj, DSc, Faculty of Mathematics and Physics, Charles University Abstract: Injective modules form a basic class studied in contemporary module theory. One of their generalizations, inspired by tilting theory, is the notion of a cotilting module. While tilting modules behave well with respect to localization, we show that colocalization is the correct approach when comparing the struc- ture of cotilting modules over commutative noetherian rings R with the structure of cotilting modules over their localizations Rm where m runs over the maximal spectrum of R. This is done in Chapter 2 of this Dissertation whose main results were published in the paper [33]. In Chapter 3, we investigate approximation properties of other classic generalizations of injective modules, the Ci- and quasi- injective modules, introduced by Harada et al. Suprisingly, we prove that these classes provide for approximations only in exceptional cases (when all Ci mod- ules are injective, or pure-injective). The Dissertation ends with a set of open problems. Keywords: Commutative noetherian ring, (co)tilting module, (generalized) injec- tive module. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:332284 |
| Date | January 2014 |
| Creators | Sahinkaya, Serap |
| Contributors | Trlifaj, Jan, Jirásko, Josef, Růžička, Pavel |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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