# Associated primes and integral closure of Noetherian rings

## TL;DR

This paper establishes criteria for prime ideals in the associated primes of certain modules over Noetherian rings and their integral closures, extending classical results to more general ring types.

## Contribution

It provides necessary and sufficient conditions for prime ideals to be in associated prime sets related to integral closures in Noetherian rings, generalizing previous classical results.

## Key findings

- Characterization of associated primes in integral closures
- Generalization of classical results for special rings
- Conditions for prime ideals in module structures

## Abstract

Let A be a Noetherian ring and B be a finitely generated A-algebra. Denote by A' the integral closure of A in B. We give necessary and sufficient conditions for prime ideals to be in Ass_{A}(B/A') and Ass_{A'}(B/A') generalizing and strengthening classical results for rings of special type.