Integral domains of rational generalized quaternion algebras
نویسندگان
چکیده
منابع مشابه
Arithmetics 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 کاملSome explicit constructions of integral structures in quaternion algebras
Let B be an undefined quaternion algebra over Q. Following the explicit chacterization of some Eichler orders in B given by Hashimoto, we define explicit embeddings of these orders in some local rings of matrices; we describe the two natural inclusions of an Eichler order of leven Nq in an Eichler order of level N . Moreover we provide a basis for a chain of Eichler orders in B and prove result...
متن کاملOperator algebras associated to integral domains
We study operator algebras associated to integral domains. In particular, with respect to a set of natural identities we look at the possible nonselfadjoint operator algebras which encode the ring structure of an integral domain. We show that these algebras give a new class of examples of semicrossed products by discrete semigroups. We investigate the structure of these algebras together with a...
متن کاملHochschild Cohomology of Algebras of Quaternion Type, I: Generalized Quaternion Groups
In terms of generators and defining relations, a description is given of the Hochschild cohomology algebra for one of the series of local algebras of quaternion type. As a corollary, the Hochschild cohomology algebra is described for the group algebras of generalized quaternion groups over algebraically closed fields of characteristic 2. Introduction Let R be a finite-dimensional algebra over a...
متن کاملQuaternion Algebras
The additive identity is (0, 0), the multiplicative identity is (1, 0), and from addition and scalar multiplication of real vectors we have (a, b) = (a, 0) + (0, b) = a(1, 0) + b(0, 1), which looks like a+ bi if we define i to be (0, 1). Real numbers occur as the pairs (a, 0). Hamilton asked himself if it was possible to multiply triples (a, b, c) in a nice way that extends multiplication of co...
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: Bulletin of the American Mathematical Society
سال: 1934
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1934-05828-2