A decomposition theory for cyclotomic modules under the complete point of view
- In 1986, D. Blessenohl and K. Johnsen (1986, J. Algebra 103, 141-159) proved that for any finite extension E/F of Galois fields there exists a complete normal basis generator w of E/F, which means that w simultaneously generates a normal basis for E over every intermediate field of E/F. In a recent monograph by the author (1997, "Finite Fields: Normal Bases and Completely Free Elements," Kluwer Academic, Boston) a theory is developed which allows the study of module structures of Galois fields as extensions with respect to various subfields and which led to an exploration of the structure of complete normal basis generators as well as explicit and algorithmic constructions of these objects. In the present paper we continue the development of that theory by providing various structural results: the Complete Decomposition Theorem, the Complete Product Theorem, a Theorem on Simultaneous Generators, and a Uniqueness Theorem.
Author: | Dirk HachenbergerORCiDGND |
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URN: | urn:nbn:de:bvb:384-opus4-8770 |
Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1021 |
Parent Title (English): | Journal of Algebra |
Type: | Article |
Language: | English |
Year of first Publication: | 2001 |
Publishing Institution: | Universität Augsburg |
Release Date: | 2008/06/20 |
Tag: | Finite field; Galois field; (complete) normal basis; (completely) free/normal element; cyclotomic module; complete/simultaneous generator |
GND-Keyword: | Galois-Feld; Galois-Erweiterung; Basis <Mathematik>; Kreiskörper |
Volume: | 237 |
Issue: | 2 |
First Page: | 470 |
Last Page: | 486 |
DOI: | https://doi.org/10.1006/jabr.2000.8609 |
Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Diskrete Mathematik, Optimierung und Operations Research | |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |