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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Representations of decomposable forms


Author: Carter Waid
Journal: Proc. Amer. Math. Soc. 43 (1974), 261-265
MSC: Primary 10C10; Secondary 10M05
DOI: https://doi.org/10.1090/S0002-9939-1974-0332656-0
MathSciNet review: 0332656
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Abstract: Results connecting binary quadratic forms and their associated quadratic fields are extended to irreducible decomposable forms and their associated fields. A rational linear substitution that carries such a form into a nonzero rational multiple of itself is shown to correspond with a linear map which admits a unique decomposition as multiplication by a nonzero element of the field followed by an automorphism of the field. This correspondence is one-to-one whenever the form is nondegenerate.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0332656-0
Keywords: Decomposable form, automorph, isometry similitude, norm form, field automorphism, Galois group
Article copyright: © Copyright 1974 American Mathematical Society

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