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On the behaviour of Brauer $p$-dimensions under finitely-generated field extensions
- Publication Year :
- 2012
- Publisher :
- arXiv, 2012.
-
Abstract
- The present paper shows that if $q \in \mathbb P$ or $q = 0$, where $\mathbb P$ is the set of prime numbers, then there exist characteristic $q$ fields $E _{q,k}\colon \ k \in \mathbb N$, of Brauer dimension Brd$(E _{q,k}) = k$ and infinite absolute Brauer $p$-dimensions abrd$_{p}(E _{q,k})$, for all $p \in \mathbb P$ not dividing $q ^{2} - q$. This ensures that Brd$_{p}(F _{q,k}) = \infty $, $p \dagger q ^{2} - q$, for every finitely-generated transcendental extension $F _{q,k}/E _{q,k}$. We also prove that each sequence $a _{p}, b _{p}$, $p \in \mathbb P$, satisfying the conditions $a _{2} = b _{2}$ and $0 \le b _{p} \le a _{p} \le \infty $, equals the sequence abrd$_{p}(E), {\rm Brd}_{p}(E)$, $p \in \mathbb P$, for a field $E$ of characteristic zero.<br />Comment: LaTeX, 14 pages: published in Journal of Algebra {\bf 428} (2015), 190-204; the abstract in the Metadata updated to fit the one of the paper
- Subjects :
- Sequence
Pure mathematics
Algebra and Number Theory
Brauer's theorem on induced characters
Zero (complex analysis)
Prime number
Field (mathematics)
Mathematics - Rings and Algebras
16K20, 16K50 (Primary), 12F20, 12J10 (Secondary)
Combinatorics
Field extension
Rings and Algebras (math.RA)
Exponent
FOS: Mathematics
Brauer group
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....2fee3a69bbc19605cd8cd29eb85845b9
- Full Text :
- https://doi.org/10.48550/arxiv.1207.0965