finite norm
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Author(s):  
Zhiyong Zheng ◽  
Man Chen ◽  
Jie Xu

It is a difficult question to generalize Gauss sums to a ring of algebraic integers of an arbitrary algebraic number field. In this paper, we define and discuss Gauss sums over a Dedekind domain of finite norm. In particular, we give a Davenport–Hasse type formula for some special Gauss sums. As an application, we give some more precise formulas for Gauss sums over the algebraic integer ring of an algebraic number field (see Theorems 4.1 and 4.2).


2012 ◽  
Vol 12 (01) ◽  
pp. 1250137 ◽  
Author(s):  
JESSE ELLIOTT

Let D be an integral domain with quotient field K. For any set X, the ring Int (DX) of integer-valued polynomials onDX is the set of all polynomials f ∈ K[X] such that f(DX) ⊆ D. Using the t-closure operation on fractional ideals, we find for any set X a D-algebra presentation of Int (DX) by generators and relations for a large class of domains D, including any unique factorization domain D, and more generally any Krull domain D such that Int (D) has a regular basis, that is, a D-module basis consisting of exactly one polynomial of each degree. As a corollary we find for all such domains D an intrinsic characterization of the D-algebras that are isomorphic to a quotient of Int (DX) for some set X. We also generalize the well-known result that a Krull domain D has a regular basis if and only if the Pólya–Ostrowski group of D (that is, the subgroup of the class group of D generated by the images of the factorial ideals of D) is trivial, if and only if the product of the height one prime ideals of finite norm q is principal for every q.


1988 ◽  
Vol 11 (4) ◽  
pp. 675-682
Author(s):  
Kairen Cai

The author applies the stress energy of differential forms to study the vanishing theorems of the Liouville type. It is shown that for a large class of underlying manifolds such as the Euclideann-space, the complexn-space, and the complex hyperbolic space form, if any vector bundle valuedp-form with conservative stress energy tensor is of finite norm or slowly divergent norm, then thep-form vanishes. This generalizes the recent results due to Hu and Sealey.


The introduction of inhomogeneity into twistor diagram theory provides a solution to the problem of defining massive states in a suitably finite way. To produce states of finite norm, however, it is necessary to make a further change in the fundamental definitions of twistor diagram theory, with the effect of introducing new inverse derivative operators.


1972 ◽  
Vol 24 (4) ◽  
pp. 557-565 ◽  
Author(s):  
Kathleen B. Levitz ◽  
Joe L. Mott

A ring A has finite norm properly, abbreviated FNP, if each proper homomorphic image of A is finite. In [3], Chew and Lawn described some of the structural properties of FNP rings with identity, which they called residually finite rings. The twofold aim of this paper is to extend the results of [3] to arbitrary rings with FNP and to give characterizations of FNP rings independent of the results of [3].If A is a ring, let A+ denote A regarded as an abelian group. In the first section of this paper, we explore the effects of FNP upon the structure of A+. The following theorem is typical of the results in this section.


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