Abstract
Let L be a proper finite Galois extension of a field K and let D be a division algebra with center K. If every subfield of D properly containing K contains a K-isomorphic copy of L, it is shown that K must be Pythagorean, L K(V - 1 ), and D is the ordinary quaternions over K. If one assumes only that every maximal subfield of D contains a K isomorphic copy of L, then, under the assumption that (D: K) is finite, it is shown that K is Pythagorean, L = K(V - 1), and D contains the ordinary quaternions over K.
Sign-in/Register to access full text options 
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.
