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Universität Augsburg
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Universität Augsburg
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Professor Dr. Wolfgang Schneider
Universität Augsburg
spricht am
Dienstag, 11. Januar 2022
um
14:15 Uhr
im
Raum 1007 (L1)
über das Thema:
| Abstract: |
| In Mod-R (R associative unitary ring) Hom has interesting substructures, called ideals respectively semi-ideals. In this talk - given in German language - we focus on the "Radical", an ideal, and the "Total", a semi-ideal containing the Radical. Originally the Total was limited to modules which are direct sums of submodules with local endomorphismenrings. For this class of modules significant relationships between the "Classical Exchange Property" and the equality of Radical and Total were discovered. This fact motivated to generalize the Total and to define new exchange properties that go great with the generalized form of the Total. The new echange properties are called "D2-Exchange Property" and "B2-Exchange Property". The goal of the talk is the presentation of the notions "Total","Radical","Classical EP", "D2-EP","B2-EP" and the mention of fundamental properties of these notions, partially with proofs. Primarily however the talk serves as a preparation for a second talk in which the deep relationships between Total/Radical on one side and D2/B2-EP on the other side will be shown in detail. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Marc Nieper-Wißkirchen |