A 2-extension of the field ℚ of rational numbersof rational numbers
Abstract It is proved that the rational number field ℚhas one, and only one, normal 2-extension ℚ(2, t8)/ℚwith group isomorphic to$$\mathbb{Z}_{2\begin{array}{*{20}c} * \\ 2 \\ \end{array} } {\mathbb{Z} \mathord{\left/ {\vphantom {\mathbb{Z} 2}} \right. \kern-\nulldelimiterspace} 2}$$.If Ωis the max...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Tsvetkov, V. M. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1999 |
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| Schlagwörter: |
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| Anmerkung: |
© Kluwer Academic/Plenum Publishers 1999 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of mathematical sciences - Kluwer Academic Publishers-Plenum Publishers, 1994, 95(1999), 2 vom: Juni, Seite 2161-2163 |
|---|---|
| Übergeordnetes Werk: |
volume:95 ; year:1999 ; number:2 ; month:06 ; pages:2161-2163 |
| Links: |
|---|
| DOI / URN: |
10.1007/BF02169978 |
|---|
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OLC2030754803 |
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| 520 | |a Abstract It is proved that the rational number field ℚhas one, and only one, normal 2-extension ℚ(2, t8)/ℚwith group isomorphic to$$\mathbb{Z}_{2\begin{array}{*{20}c} * \\ 2 \\ \end{array} } {\mathbb{Z} \mathord{\left/ {\vphantom {\mathbb{Z} 2}} \right. \kern-\nulldelimiterspace} 2}$$.If Ωis the maximal subfield of a real-closed field, which does not contain$$\sqrt 2 $$,then the algebraic closure$$\bar \Omega $$of Ωis isomorphic to the field$$\Omega \begin{array}{*{20}c} \otimes \\ \mathbb{Q} \\ \end{array} \mathbb{Q}_{(2,\infty )} $$.Bibliography: 7titles. | ||
| 650 | 4 | |a Rational Number | |
| 650 | 4 | |a Number Field | |
| 650 | 4 | |a Algebraic Closure | |
| 650 | 4 | |a Maximal Subfield | |
| 650 | 4 | |a Rational Number Field | |
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10.1007/BF02169978 doi (DE-627)OLC2030754803 (DE-He213)BF02169978-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Tsvetkov, V. M. verfasserin aut A 2-extension of the field ℚ of rational numbersof rational numbers 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic/Plenum Publishers 1999 Abstract It is proved that the rational number field ℚhas one, and only one, normal 2-extension ℚ(2, t8)/ℚwith group isomorphic to$$\mathbb{Z}_{2\begin{array}{*{20}c} * \\ 2 \\ \end{array} } {\mathbb{Z} \mathord{\left/ {\vphantom {\mathbb{Z} 2}} \right. \kern-\nulldelimiterspace} 2}$$.If Ωis the maximal subfield of a real-closed field, which does not contain$$\sqrt 2 $$,then the algebraic closure$$\bar \Omega $$of Ωis isomorphic to the field$$\Omega \begin{array}{*{20}c} \otimes \\ \mathbb{Q} \\ \end{array} \mathbb{Q}_{(2,\infty )} $$.Bibliography: 7titles. Rational Number Number Field Algebraic Closure Maximal Subfield Rational Number Field Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 95(1999), 2 vom: Juni, Seite 2161-2163 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:95 year:1999 number:2 month:06 pages:2161-2163 https://doi.org/10.1007/BF02169978 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4310 31.00 VZ AR 95 1999 2 06 2161-2163 |
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10.1007/BF02169978 doi (DE-627)OLC2030754803 (DE-He213)BF02169978-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Tsvetkov, V. M. verfasserin aut A 2-extension of the field ℚ of rational numbersof rational numbers 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic/Plenum Publishers 1999 Abstract It is proved that the rational number field ℚhas one, and only one, normal 2-extension ℚ(2, t8)/ℚwith group isomorphic to$$\mathbb{Z}_{2\begin{array}{*{20}c} * \\ 2 \\ \end{array} } {\mathbb{Z} \mathord{\left/ {\vphantom {\mathbb{Z} 2}} \right. \kern-\nulldelimiterspace} 2}$$.If Ωis the maximal subfield of a real-closed field, which does not contain$$\sqrt 2 $$,then the algebraic closure$$\bar \Omega $$of Ωis isomorphic to the field$$\Omega \begin{array}{*{20}c} \otimes \\ \mathbb{Q} \\ \end{array} \mathbb{Q}_{(2,\infty )} $$.Bibliography: 7titles. Rational Number Number Field Algebraic Closure Maximal Subfield Rational Number Field Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 95(1999), 2 vom: Juni, Seite 2161-2163 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:95 year:1999 number:2 month:06 pages:2161-2163 https://doi.org/10.1007/BF02169978 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4310 31.00 VZ AR 95 1999 2 06 2161-2163 |
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10.1007/BF02169978 doi (DE-627)OLC2030754803 (DE-He213)BF02169978-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Tsvetkov, V. M. verfasserin aut A 2-extension of the field ℚ of rational numbersof rational numbers 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic/Plenum Publishers 1999 Abstract It is proved that the rational number field ℚhas one, and only one, normal 2-extension ℚ(2, t8)/ℚwith group isomorphic to$$\mathbb{Z}_{2\begin{array}{*{20}c} * \\ 2 \\ \end{array} } {\mathbb{Z} \mathord{\left/ {\vphantom {\mathbb{Z} 2}} \right. \kern-\nulldelimiterspace} 2}$$.If Ωis the maximal subfield of a real-closed field, which does not contain$$\sqrt 2 $$,then the algebraic closure$$\bar \Omega $$of Ωis isomorphic to the field$$\Omega \begin{array}{*{20}c} \otimes \\ \mathbb{Q} \\ \end{array} \mathbb{Q}_{(2,\infty )} $$.Bibliography: 7titles. Rational Number Number Field Algebraic Closure Maximal Subfield Rational Number Field Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 95(1999), 2 vom: Juni, Seite 2161-2163 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:95 year:1999 number:2 month:06 pages:2161-2163 https://doi.org/10.1007/BF02169978 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4310 31.00 VZ AR 95 1999 2 06 2161-2163 |
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10.1007/BF02169978 doi (DE-627)OLC2030754803 (DE-He213)BF02169978-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Tsvetkov, V. M. verfasserin aut A 2-extension of the field ℚ of rational numbersof rational numbers 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic/Plenum Publishers 1999 Abstract It is proved that the rational number field ℚhas one, and only one, normal 2-extension ℚ(2, t8)/ℚwith group isomorphic to$$\mathbb{Z}_{2\begin{array}{*{20}c} * \\ 2 \\ \end{array} } {\mathbb{Z} \mathord{\left/ {\vphantom {\mathbb{Z} 2}} \right. \kern-\nulldelimiterspace} 2}$$.If Ωis the maximal subfield of a real-closed field, which does not contain$$\sqrt 2 $$,then the algebraic closure$$\bar \Omega $$of Ωis isomorphic to the field$$\Omega \begin{array}{*{20}c} \otimes \\ \mathbb{Q} \\ \end{array} \mathbb{Q}_{(2,\infty )} $$.Bibliography: 7titles. Rational Number Number Field Algebraic Closure Maximal Subfield Rational Number Field Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 95(1999), 2 vom: Juni, Seite 2161-2163 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:95 year:1999 number:2 month:06 pages:2161-2163 https://doi.org/10.1007/BF02169978 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4310 31.00 VZ AR 95 1999 2 06 2161-2163 |
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10.1007/BF02169978 doi (DE-627)OLC2030754803 (DE-He213)BF02169978-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Tsvetkov, V. M. verfasserin aut A 2-extension of the field ℚ of rational numbersof rational numbers 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic/Plenum Publishers 1999 Abstract It is proved that the rational number field ℚhas one, and only one, normal 2-extension ℚ(2, t8)/ℚwith group isomorphic to$$\mathbb{Z}_{2\begin{array}{*{20}c} * \\ 2 \\ \end{array} } {\mathbb{Z} \mathord{\left/ {\vphantom {\mathbb{Z} 2}} \right. \kern-\nulldelimiterspace} 2}$$.If Ωis the maximal subfield of a real-closed field, which does not contain$$\sqrt 2 $$,then the algebraic closure$$\bar \Omega $$of Ωis isomorphic to the field$$\Omega \begin{array}{*{20}c} \otimes \\ \mathbb{Q} \\ \end{array} \mathbb{Q}_{(2,\infty )} $$.Bibliography: 7titles. Rational Number Number Field Algebraic Closure Maximal Subfield Rational Number Field Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 95(1999), 2 vom: Juni, Seite 2161-2163 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:95 year:1999 number:2 month:06 pages:2161-2163 https://doi.org/10.1007/BF02169978 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4310 31.00 VZ AR 95 1999 2 06 2161-2163 |
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A 2-extension of the field ℚ of rational numbersof rational numbers |
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Abstract It is proved that the rational number field ℚhas one, and only one, normal 2-extension ℚ(2, t8)/ℚwith group isomorphic to$$\mathbb{Z}_{2\begin{array}{*{20}c} * \\ 2 \\ \end{array} } {\mathbb{Z} \mathord{\left/ {\vphantom {\mathbb{Z} 2}} \right. \kern-\nulldelimiterspace} 2}$$.If Ωis the maximal subfield of a real-closed field, which does not contain$$\sqrt 2 $$,then the algebraic closure$$\bar \Omega $$of Ωis isomorphic to the field$$\Omega \begin{array}{*{20}c} \otimes \\ \mathbb{Q} \\ \end{array} \mathbb{Q}_{(2,\infty )} $$.Bibliography: 7titles. © Kluwer Academic/Plenum Publishers 1999 |
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Abstract It is proved that the rational number field ℚhas one, and only one, normal 2-extension ℚ(2, t8)/ℚwith group isomorphic to$$\mathbb{Z}_{2\begin{array}{*{20}c} * \\ 2 \\ \end{array} } {\mathbb{Z} \mathord{\left/ {\vphantom {\mathbb{Z} 2}} \right. \kern-\nulldelimiterspace} 2}$$.If Ωis the maximal subfield of a real-closed field, which does not contain$$\sqrt 2 $$,then the algebraic closure$$\bar \Omega $$of Ωis isomorphic to the field$$\Omega \begin{array}{*{20}c} \otimes \\ \mathbb{Q} \\ \end{array} \mathbb{Q}_{(2,\infty )} $$.Bibliography: 7titles. © Kluwer Academic/Plenum Publishers 1999 |
| abstract_unstemmed |
Abstract It is proved that the rational number field ℚhas one, and only one, normal 2-extension ℚ(2, t8)/ℚwith group isomorphic to$$\mathbb{Z}_{2\begin{array}{*{20}c} * \\ 2 \\ \end{array} } {\mathbb{Z} \mathord{\left/ {\vphantom {\mathbb{Z} 2}} \right. \kern-\nulldelimiterspace} 2}$$.If Ωis the maximal subfield of a real-closed field, which does not contain$$\sqrt 2 $$,then the algebraic closure$$\bar \Omega $$of Ωis isomorphic to the field$$\Omega \begin{array}{*{20}c} \otimes \\ \mathbb{Q} \\ \end{array} \mathbb{Q}_{(2,\infty )} $$.Bibliography: 7titles. © Kluwer Academic/Plenum Publishers 1999 |
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| title_short |
A 2-extension of the field ℚ of rational numbersof rational numbers |
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2024-07-04T02:54:26.296Z |
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