The Maximal Orders of Generalized Quaternion Division Algebras
نویسندگان
چکیده
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...
متن کاملHyperbolicity of orders of quaternion algebras and group rings
For a given division algebra of the quaternions, we construct two types of units of its Z-orders: Pell units and Gauss units. Also, if K = Q √ −d, d ∈ Z \ {0, 1} is square free and R = IK , we classify R and G such that U1(RG) is hyperbolic. In particular, we prove that U1(RK8) is hyperbolic iff d > 0 and d ≡ 7 (mod 8). In this case, the hyperbolic boundary ∂(U1(RG)) ∼= S, the two dimensional s...
متن کاملArithmetics of Rational Generalized Quaternion Algebras
a0 is called the real part of Q. An arithmetic S of Q(a, ]8) is a set of numbers having the following properties : Ca : S is closed with respect to algebraic addition. Cm: S is closed with respect to multiplication. R: For every number of 5, (4) has integral coefficients. U: 5 contains I0 , Ii and I2 (and hence I i l 2 by Cm). M : 5 is maximal ; that is, S is contained in no larger set having P...
متن کاملNoetherian semigroup algebras and prime maximal orders
Let S be a semigroup and K be a field. A K-space K[S], with basis S and with multiplication extending, in a natural way, the operation on S, is called a semigroup algebra. It remains an open problem to characterize semigroup algebras that are a prime Noetherian maximal order. In this thesis, we give an answer to the problem for a large class of cancellative semigroups and we illustrate these re...
متن کاملSome Remarks on Representations of Quaternion Division Algebras
For the quaternion division algebra D over a non-Archimedean local field k, and π an irreducible finite dimensional representation of D×, say with trivial central character, we prove the existence of a quadratic extension K of k such that the trivial character of K× appears in π, as well as the existence of a quadratic extension L of k such that the trivial character of L× does not appear in π....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1936
ISSN: 0002-9947
DOI: 10.2307/1989661