Abstract
Letkbe any field,s=(aij)1≤i,j≤n+1∈GLn+1(k),K≔k(x1/xn+1,···,xn/xn+1,y1/yn+1,···,yn/yn+1) a field extension of transcendence degree 2noverk. The diagonal action ofsonKis defined as[Equation] [Equation]Theorem.There existz1,⋯,zn∈Ksuch thatK=k(x1/xn+1,···,xn/xn+1,z1,⋯,zn) ands(zi)=zifor 1≤i≤n. In particular, ifk(x1/xn+1,⋯,xn/xn+1)〈s〉is rational (=purely transcendental) overk, so isK〈s〉overk.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
