# Idealtheorie in Ringbereichen

@article{NoetherIdealtheorieIR,
title={Idealtheorie in Ringbereichen},
author={Emmy Noether},
journal={Mathematische Annalen},
volume={83},
pages={24-66}
}
• E. Noether
• Published 1 March 1921
• Mathematics
• Mathematische Annalen
162 Citations

### 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 $\sigma$ an

### 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 ring

### 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 ring

### 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.

### J an 2 01 9 From analytical mechanical problems to rewriting theory through

• Mathematics
• 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 developed

### 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 developed

### 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 categories

### 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

### Symbolic Rees Algebras

• Mathematics
Commutative Algebra
• 2021
We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a

## References

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### 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 V

### 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 von

• J.'f. M
• 1919

### ~, gleich der Einheitsklasse und sind folglich bei der Zerlegmug wegzulassen; das gleiche gilt flit ~o +, wenn ~ --~ n ist

• Ist r etwa r~ -~-r~ + ~