# Idealtheorie in Ringbereichen

@article{NoetherIdealtheorieIR,
title={Idealtheorie in Ringbereichen},
author={E. Noether},
journal={Mathematische Annalen},
volume={83},
pages={24-66}
}
156 Citations

#### Paper Mentions

Completely generalized right primary rings and their extensions
A ring $R$ is said to be a completely generalized right primary ring ($c.g.r.p$ ring) if $a, b \in R$ with $ab = 0$ implies that $a = 0$ or $b$ is nilpotent. Let now $R$ be a ring and $\sigma$ anExpand
On the index of reducibility in Noetherian modules
• Mathematics
• 2014
Let M be a finitely generated module over a Noetherian ring R and N be a submodule. The index of reducibility irM(N) is the number of irreducible submodules that appear in an irredundant irreducibleExpand
Commutative ideal theory without finiteness conditions : Completely irreducible ideals
• Mathematics
• 2006
An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ringExpand
COMMUTATIVE IDEAL THEORY WITHOUT FINITENESS CONDITIONS :
An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ringExpand
The irreducible multiplicity and Ulrich modules
• Mathematics
• 2021
In this paper, we give a relation between the Hilbert multiplicity and the irreducible multiplicity. As an application, we characterize Ulrich modules in term of the irreducible multiplicity.
From Analytical Mechanics Problems to Rewriting Theory Through M. Janet’s Work
• Mathematics
• 2020
This chapter is devoted to a survey of the historical background of Grobner bases for D-modules and linear rewriting theory largely developed in algebra throughout the twentieth century and toExpand
J an 2 01 9 From analytical mechanical problems to rewriting theory through
• 2018
This note surveys the historical background of the Gröbner basis theory for D-modules and linear rewriting theory. The objective is to present a deep interaction of these two fields largely developedExpand
From analytical mechanical problems to rewriting theory through M. Janet
• Mathematics
• 2017
This note surveys the historical background of the Gröbner basis theory for D-modules and linear rewriting theory. The objective is to present a deep interaction of these two fields largely developedExpand
Categorical and homological aspects of module theory over commutative rings
The purpose of this work is to understand the structure of the subcategories of mod(R) and the derived category D(R) for a commutative Noetherian ring R. Special focus is given to categoriesExpand
A Survey on Combinatorial Duality Approach to Zero-dimensional Ideals
A Survey on Combinatorial Duality Approach to Zero-dimensional Ideals. ——————————— theomora@dima.unige.it ——————————— theomora@dima.unige.it

#### References

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Über die Teiler der Null und die Zerlegung von Ringen.
E i n l e i t u n g . Seit langem sind in die Arithmetik neben den sogenannten Körpern, in denen alle gewöhnlichen Rechengesetze wie für die rationalen Zahlen gelten, auch verschiedene Bereiche vonExpand
Ueber die vollen Invariantensysteme
Meine Abhandlung „ Uber die Theorie der algebraischen Formen“1 enthalt eine Reihe von Theoremen, welche fur die Theorie der algebraischen Invarianten von Bedeutung sind. Insbesondere in Abschnitt VExpand