In the setting of Noetherian or Dedekind domains, we investigate the properties of very flat and contraadjusted modules. These are the modules from the respective classes in the cotorsion pair (VF, CA) generated by the set of all modules of the form R[s−1 ]. Furthermore, we introduce the concept of locally very flat modules and pursue the analogy of their relation to very flat modules and the relation between projective and flat Mittag-Leffler modules. It is shown that for Noetherian domains, the class of all very flat modules is covering, if and only if the class of all locally very flat modules is precovering, if and only if the spectrum of the ring is finite; for domains of cardinality less than 2ω , this is further equivalent to the class of all contraadjusted modules being enveloping.
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:347806 |
| Date | January 2015 |
| Creators | Slávik, Alexander |
| Contributors | Trlifaj, Jan, Šťovíček, Jan |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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