Berstel and Reutenauer stated the iteration theorem for recognizable formal power series on trees over fields and vector spaces. The key idea of its proof is the existence of pseudo-regular matrices in matrix-products. This theorem is generalized to integral domains and modules over integral domains in this thesis. It only requires the reader to have basic knowledge in linear algebra. Concepts from the advanced linear algebra and abstract algebra are introduced in the preliminary chapter.:1. Introduction
2. Preliminaries
3. Long products of matrices
4. Formal power series on trees
5. The generalized iteration theorem
6. Conclusion
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:88029 |
| Date | 15 November 2023 |
| Creators | Kramer, Patrick |
| Contributors | Maletti, Andreas, Universität Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/acceptedVersion, doc-type:bachelorThesis, info:eu-repo/semantics/bachelorThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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