|
Algebra and Discrete Mathematics, 2003, выпуск 3, страницы 1–6
(Mi adm381)
|
|
|
|
RESEARCH ARTICLE
$N$ – real fields
Shalom Feigelstock Department of Mathematics, Bar–Ilan University, Ramat Gan,
Israel
Аннотация:
A field $F$ is $n$-real if $-1$ is not the sum of $n$ squares in $F$. It is shown that a field $F$ is $m$-real if and only if $\text{rank }(AA^t)=\text{rank }(A)$ for every $n\times m$ matrix $A$ with entries from $F$. An $n$-real field $F$ is $n$-real closed if every proper algebraic extension of $F$ is not $n$-real. It is shown that if a $3$-real field $F$ is $2$-real closed, then $F$ is a real closed field. For $F$ a quadratic extension of the field of rational numbers, the greatest integer $n$ such that $F$ is $n$-real is determined.
Ключевые слова:
$n$-real, $n$-real closed.
Поступила в редакцию: 03.03.2003 Исправленный вариант: 23.10.2003
Образец цитирования:
Shalom Feigelstock, “$N$ – real fields”, Algebra Discrete Math., 2003, no. 3, 1–6
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm381 https://www.mathnet.ru/rus/adm/y2003/i3/p1
|
Статистика просмотров: |
Страница аннотации: | 136 | PDF полного текста: | 44 | Первая страница: | 1 |
|