Matches in SemOpenAlex for { <https://semopenalex.org/work/W2784922111> ?p ?o ?g. }
Showing items 1 to 78 of
78
with 100 items per page.
- W2784922111 abstract "Let $k$ be an infinite field such that char $kneq 2$ and $k$ is not algebraically closed. Let $ain ksetminus k^2$ and $L=k(sqrt{a})(x,y)$ be a field extension of $k$ where $x,y$ are algebraically independent over $k$. Assume that $sigma$ is a $k$-automorphism on $L$ defined by [ sigma: sqrt{a}mapsto -sqrt{a}, xmapsto frac{b}{x}, ymapsto frac{c(x+frac{b}{x})+d}{y} ] where $b,c,d in k$, $bneq 0$ and at least one of $c,d$ is non-zero. Theorem. Let $L^{langlesigmarangle}={uin L:sigma(u)=u}$ be the fixed subfield of $L$. Assume that $b in ksetminus k^2$. Then the field $L^{langlesigmarangle}$ is rational (resp. stably rational, unirational) over $k$ if and only if there exist $alpha, beta, gamma, deltain k$ such that $alpha ^2-a beta ^2=b$, $gamma^2-a delta ^2= 2c alpha + d$. The same question when $b$ is a square in $k$ is solved also." @default.
- W2784922111 created "2018-02-02" @default.
- W2784922111 creator A5014289480 @default.
- W2784922111 creator A5036512098 @default.
- W2784922111 creator A5038464497 @default.
- W2784922111 creator A5039044067 @default.
- W2784922111 date "2018-01-20" @default.
- W2784922111 modified "2023-09-27" @default.
- W2784922111 title "A two-dimensional rationality problem" @default.
- W2784922111 cites W1493035006 @default.
- W2784922111 cites W1571322445 @default.
- W2784922111 cites W1971603717 @default.
- W2784922111 cites W2006287522 @default.
- W2784922111 cites W2011882525 @default.
- W2784922111 cites W2034145091 @default.
- W2784922111 cites W2101306245 @default.
- W2784922111 cites W2146372699 @default.
- W2784922111 cites W2326305241 @default.
- W2784922111 cites W2430799059 @default.
- W2784922111 cites W2510704568 @default.
- W2784922111 cites W2962868159 @default.
- W2784922111 cites W2964101755 @default.
- W2784922111 cites W2964271407 @default.
- W2784922111 cites W3144623956 @default.
- W2784922111 hasPublicationYear "2018" @default.
- W2784922111 type Work @default.
- W2784922111 sameAs 2784922111 @default.
- W2784922111 citedByCount "0" @default.
- W2784922111 crossrefType "posted-content" @default.
- W2784922111 hasAuthorship W2784922111A5014289480 @default.
- W2784922111 hasAuthorship W2784922111A5036512098 @default.
- W2784922111 hasAuthorship W2784922111A5038464497 @default.
- W2784922111 hasAuthorship W2784922111A5039044067 @default.
- W2784922111 hasConcept C114614502 @default.
- W2784922111 hasConcept C118712358 @default.
- W2784922111 hasConcept C121332964 @default.
- W2784922111 hasConcept C202444582 @default.
- W2784922111 hasConcept C203701370 @default.
- W2784922111 hasConcept C2778049214 @default.
- W2784922111 hasConcept C33923547 @default.
- W2784922111 hasConcept C62520636 @default.
- W2784922111 hasConcept C9652623 @default.
- W2784922111 hasConceptScore W2784922111C114614502 @default.
- W2784922111 hasConceptScore W2784922111C118712358 @default.
- W2784922111 hasConceptScore W2784922111C121332964 @default.
- W2784922111 hasConceptScore W2784922111C202444582 @default.
- W2784922111 hasConceptScore W2784922111C203701370 @default.
- W2784922111 hasConceptScore W2784922111C2778049214 @default.
- W2784922111 hasConceptScore W2784922111C33923547 @default.
- W2784922111 hasConceptScore W2784922111C62520636 @default.
- W2784922111 hasConceptScore W2784922111C9652623 @default.
- W2784922111 hasLocation W27849221111 @default.
- W2784922111 hasOpenAccess W2784922111 @default.
- W2784922111 hasPrimaryLocation W27849221111 @default.
- W2784922111 hasRelatedWork W1926082235 @default.
- W2784922111 hasRelatedWork W2014690786 @default.
- W2784922111 hasRelatedWork W2047701775 @default.
- W2784922111 hasRelatedWork W2099158205 @default.
- W2784922111 hasRelatedWork W2260530353 @default.
- W2784922111 hasRelatedWork W2284510939 @default.
- W2784922111 hasRelatedWork W2344403768 @default.
- W2784922111 hasRelatedWork W2514553353 @default.
- W2784922111 hasRelatedWork W2568046207 @default.
- W2784922111 hasRelatedWork W2751768203 @default.
- W2784922111 hasRelatedWork W2786447966 @default.
- W2784922111 hasRelatedWork W2887070687 @default.
- W2784922111 hasRelatedWork W2900240983 @default.
- W2784922111 hasRelatedWork W2949861741 @default.
- W2784922111 hasRelatedWork W2949888424 @default.
- W2784922111 hasRelatedWork W3022263852 @default.
- W2784922111 hasRelatedWork W3030047316 @default.
- W2784922111 hasRelatedWork W3036966200 @default.
- W2784922111 hasRelatedWork W3098422168 @default.
- W2784922111 hasRelatedWork W3125729000 @default.
- W2784922111 isParatext "false" @default.
- W2784922111 isRetracted "false" @default.
- W2784922111 magId "2784922111" @default.
- W2784922111 workType "article" @default.