In this paper, we determine completely the initial Fitting ideal of the minus part of the ideal class group of an abelian number field over Q up to the 2-component. This answers an open question of Mazur and Wiles [11] up to the 2-component, and proves Conjecture 0.1 in [8]. We also study Brumer’s conjecture and prove a stronger version for a CM-field, assuming certain conditions, in particular...

Abstract We completely calculate the Fitting ideal of classical p -ramified Iwasawa module for any abelian extension K / k totally real fields, using shifted ideals recently developed by second author. This generalizes former results where we had to assume that only -adic places may ramify in . One important ingredients is computation some complexes appropriate derived categories.

manuscripta mathematica manuscript No. Abstract. The core of a projective dimension one module is computed explicitly in terms of Fitting ideals. In particular, our formula recovers previous work by R. Mohan on integrally closed torsionfree modules over a two-dimensional regular local ring.

We develop an algorithm for computing numerical evidence for a conjecture whose validity is predicted by the requirement that the Equivariant Tamagawa Number conjectures for Tate motives as formulated by Burns and Flach are compatible with the functional equation of Artin Ä-series. The algorithm includes methods for the computation of Fitting ideals and projective lattices over the integral gro...

For any finitely generated torsion-free graded module over a polynomial ring, there exists a homogeneous ideal fitting into an exact sequence similar to a Bourbaki sequence even though its height is not restricted to two.

A finitely generated $R$-module is said to be a module of type ($F_r$) if its $(r-1)$-th Fitting ideal is the zero ideal and its $r$-th Fitting ideal is a regular ideal. Let $R$ be a commutative ring and $N$ be a submodule of  $R^n$ which is generated by columns of  a matrix $A=(a_{ij})$ with $a_{ij}in R$ for all $1leq ileq n$, $jin Lambda$, where $Lambda $ is a (possibly infinite) index set.  ...

generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and   -fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. some new results are obtained.