On a Class of Quaternion Algebras |
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2a which represent aw₂ b'xy b₁ B₂i bx'y C₁ class of forms class of ideals class of left complex integers conjugate contains no square Dickson discriminant 2a discriminant of ƒ division algebra elements in G F represents form a proper form corresponding form ƒ forms ax2 ƒ is equivalent Hence ƒ hermitian forms Hurwitz integral ideal is equivalent ideals in G indefinite primitive integral elements integral quaternions JAMES H. D. TELLER L₁ Latimer Latimer's left ideals LEMMA mod a₁ N(w₁ odd prime odd rational integer phrase non-singular positive odd rational prime to a₁ primitive form primitive indefinite form principal ideal proper basis w₁ prove THEOREM QUATERNION ALGEBRAS range over G represent positive integers represents a positive shown that N(2 t₁w₁ ternary form tizw₂ uniquely determined unit left factor UNIVERSITY OF KENTUCKY w₂ xw₁ y₁