‎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...

A function field over a finite field is called maximal if it achieves the Hasse-Weil bound. Finding possible genera that maximal function fields achieve has both theoretical interest and practical applications to coding theory and other topics. As a subfield of a maximal function field is also maximal, one way to find maximal function fields is to find all subfields of a maximal function field....

Let p be a prime integer and F the function field in two algebraically independent variables over smaller F0. We prove that if char(F0)=p⩾3 then there exist p2−1 cyclic algebras of degree have no maximal subfield common, char(F0)=0 p2 common.

We show that the Ree unital R ( q ) has an embedding in a projective plane over field F if and only = 3 8 is subfield of . In this case, unique up to linear transformations. Besides elementary calculations, our proof uses classification maximal subgroups simple groups.

We describe a new class of maximal cliques, with vector space structure, Cayley graphs defined on the additive group field. In particular, we show that in cubic Paley graph order $q^3$, subfield $q$ elements forms clique. Similar statements also hold for quadruple and Peisert quartic order.

We develop an efficient technique for computing values at s = 1 of Hecke L-functions. We apply this technique to the computation of relative class numbers of non-abelian CM-fields N which are abelian extensions of some totally real subfield L. We note that the smaller the degree of L the more efficient our technique is. In particular, our technique is very efficient whenever instead of simply c...