Flows in graphs and the homology of free categories
We study the \(R\)-module of generalized flows in a graph with coefficients in the \(R\)-representation of the graph over a ring \(R\) with 1 and show that this \(R\)-module is isomorphic to the first derived functor of the colimit. We generalize Kirchhoff’s laws and build an exact sequence for calc...
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| Datum: | 2018 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/957 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | We study the \(R\)-module of generalized flows in a graph with coefficients in the \(R\)-representation of the graph over a ring \(R\) with 1 and show that this \(R\)-module is isomorphic to the first derived functor of the colimit. We generalize Kirchhoff’s laws and build an exact sequence for calculating the R-module of flows in the union of graphs. |
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