منابع مشابه
Maximally Complete Fields
Kaplansky proved in 1942 that among ail fields with a valuation having a given divisible value group G, a given algebraically closed residue field R, and a given restriction to the minimal subfield (either the trivial valuation on Qor Fp , or the /?-adic valuation on Q), there is one that is maximal in the strong sensé that every other can be embedded in it. In this paper, we construct this fie...
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The probability for two monic polynomials of a positive degree n with coefficients in the finite field Fq to be relatively prime turns out to be identical with the probability for an n × n Hankel matrix over Fq to be nonsingular. Motivated by this, we give an explicit map from pairs of coprime polynomials to nonsingular Hankel matrices that explains this connection. A basic tool used here is th...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1958
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500010828