منابع مشابه
On normalizers of maximal subfields of division algebras
Here, we investigate a conjecture posed by Amiri and Ariannejad claiming that if every maximal subfield of a division ring $D$ has trivial normalizer, then $D$ is commutative. Using Amitsur classification of finite subgroups of division rings, it is essentially shown that if $D$ is finite dimensional over its center then it contains a maximal subfield with non-trivial normalize...
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One of the most elementary consequences of the assumption that a normal division algebra A is cyclic of degree n over its centrum K is that A contains a quantity j whose minimum equation is co=7 in K. In 1933 I conjectured the truth of the converse proposition. The proof is easily reducible f to the case where n is a power p of a prime p. Let a be the characteristic of K. I succeeded in proving...
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We prove that the following are equivalent. We denote by Pq the vector space of functions from a finite field Fq to itself, which can be represented as the space Pq := Fq[x]/(x q − x) of polynomial functions. We denote by On ⊂ Pq the set of polynomials that are either the zero polynomial, or have at most n distinct roots in Fq. Given two subspaces Y,Z of Pq, we denote by 〈Y,Z〉 their span. • Let...
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It is well known that the set of separable pure states is measure 0 in the set of pure states. Herein we extend this fact and show that the set of rank r separable states is measure 0 in the set of rank r states provided r is not maximal rank. Recently quite a few authors have looked at low rank separable and entangled states. (See [1] and the references therein and [2].) Therefore it makes sen...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1978
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1978-0460300-4