Maximal orders over Krull domains
نویسندگان
چکیده
منابع مشابه
Power Series over Generalized Krull Domains
We resolve an open problem in commutative algebra and Field Arithmetic, posed by Jarden – Let R be a generalized Krull domain. Is the ring R[[X]] of formal power series over R a generalized Krull domain? We show that the answer is negative.
متن کاملA Mordell Inequality for Lattices over Maximal Orders
In this paper we prove an analogue of Mordell’s inequality for lattices in finite-dimensional complex or quaternionic Hermitian space that are modules over a maximal order in an imaginary quadratic number field or a totally definite rational quaternion algebra. This inequality implies that 16dimensional Barnes-Wall lattice has optimal density among all 16-dimensional lattices with Hurwitz struc...
متن کاملMaximal Crossed Product Orders over Discrete Valuation Rings
The problem of determining when a (classical) crossed product T = S ∗ G of a finite group G over a discrete valuation ring S is a maximal order, was answered in the 1960’s for the case where S is tamely ramified over the subring of invariants S. The answer was given in terms of the conductor subgroup (with respect to f) of the inertia. In this paper we solve this problem in general when S/S is ...
متن کاملThe Construction of Maximal Orders Over a Dedekind Domain
Suppose R is a complete local Dedekind domain with quotient field F, and let f(x) be a monic polynomial in R[x] having non-zero discriminant. We present here a new algorithm to construct the maximal order of the algebra Af = F[x]/f(x)F[x]. The new algorithm incorporates ideas of Zassenhaus (1975, 1980) concerning P-adic stability and the algebraic decomposition of A s . We show that it is alway...
متن کاملMaximal Orders in Semigroups1
Inspired by the ring theory concepts of orders and classical rings of quotients, Fountain and Petrich introduced the notion of a completely 0-simple semigroup of quotients in [19]. This was generalised to a much wider class of semigroups by Gould in [20]. The notion extends the well known concept of group of quotients [8]. To give the definition we first have to explain what is meant by a squar...
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: Journal of Algebra
سال: 1968
ISSN: 0021-8693
DOI: 10.1016/0021-8693(68)90083-5