Certain simple maximal subfields in division rings

Mehdi Aaghabali; Mai Hoang Bien

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 4, page 1053-1060
  • ISSN: 0011-4642

Abstract

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Let D be a division ring finite dimensional over its center F . The goal of this paper is to prove that for any positive integer n there exists a ∈ D ( n ) , the n th multiplicative derived subgroup such that F ( a ) is a maximal subfield of D . We also show that a single depth- n iterated additive commutator would generate a maximal subfield of D .

How to cite

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Aaghabali, Mehdi, and Bien, Mai Hoang. "Certain simple maximal subfields in division rings." Czechoslovak Mathematical Journal 69.4 (2019): 1053-1060. <http://eudml.org/doc/294200>.

@article{Aaghabali2019,
abstract = {Let $D$ be a division ring finite dimensional over its center $F$. The goal of this paper is to prove that for any positive integer $n$ there exists $a\in D^\{(n)\},$ the $n$th multiplicative derived subgroup such that $F(a)$ is a maximal subfield of $D$. We also show that a single depth-$n$ iterated additive commutator would generate a maximal subfield of $D.$},
author = {Aaghabali, Mehdi, Bien, Mai Hoang},
journal = {Czechoslovak Mathematical Journal},
keywords = {division ring; rational identity; maximal subfield},
language = {eng},
number = {4},
pages = {1053-1060},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Certain simple maximal subfields in division rings},
url = {http://eudml.org/doc/294200},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Aaghabali, Mehdi
AU - Bien, Mai Hoang
TI - Certain simple maximal subfields in division rings
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 1053
EP - 1060
AB - Let $D$ be a division ring finite dimensional over its center $F$. The goal of this paper is to prove that for any positive integer $n$ there exists $a\in D^{(n)},$ the $n$th multiplicative derived subgroup such that $F(a)$ is a maximal subfield of $D$. We also show that a single depth-$n$ iterated additive commutator would generate a maximal subfield of $D.$
LA - eng
KW - division ring; rational identity; maximal subfield
UR - http://eudml.org/doc/294200
ER -

References

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  8. Hai, B. X., Dung, T. H., Bien, M. H., Almost subnormal subgroups in division rings with generalized algebraic rational identities, Available at https://arxiv.org/abs/1709.04774. 
  9. Lam, T. Y., 10.1007/978-1-4419-8616-0, Graduate Texts in Mathematics 131, Springer, New York (2001). (2001) Zbl0980.16001MR1838439DOI10.1007/978-1-4419-8616-0
  10. Mahdavi-Hezavehi, M., 10.1080/00927879508825257, Commun. Algebra 23 (1995), 913-926. (1995) Zbl0833.16014MR1316740DOI10.1080/00927879508825257
  11. Mahdavi-Hezavehi, M., Commutators in division rings revisited, Bull. Iran. Math. Soc. 26 (2000), 7-88. (2000) Zbl0983.16012MR1828953
  12. Mahdavi-Hezavehi, M., Akbari-Feyzaabaadi, S., Mehraabaadi, M., Hajie-Abolhassan, H., 10.1080/00927879508825374, Commun. Algebra 23 (1995), 2881-2887. (1995) Zbl0866.16012MR1332151DOI10.1080/00927879508825374
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