Brauer's class number relation

Fuzzy number-valued fuzzy ‎relation

It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...

Class-number Problems for Cubic Number Fields

Kuroda’s Class Number Formula

Let k be a number field and K/k a V4-extension, i.e., a normal extension with Gal(K/k) = V4, where V4 is Klein’s four-group. K/k has three intermediate fields, say k1, k2, and k3. We will use the symbol N i (resp. Ni) to denote the norm of K/ki (resp. ki/k), and by a widespread abuse of notation we will apply N i and Ni not only to numbers, but also to ideals and ideal classes. The unit groups ...

fuzzy number-valued fuzzy ‎relation

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

Discriminants of Hermitian R[G]-modules and Brauer’s Class Number Relation

The purpose of this paper is to lay the foundations for a quantitative theory of relations among discriminants of hermitian RG-modules which are induced by character relations. This is accomplished by introducing an invariant δ(M) attached to an RG-module M which plays the role of a correction term in such relations and to study its functorial properties such as localization and induction theor...