| Saturday 20 April 2024 | |
| Events for day: Thursday 31 December 2020 |
| 11:00 - 12:00 Commutative Algebra Webinars Strongly Irreducible Submodules in the Arithmetical and Noetherian Modules School MATHEMATICS Let $R$ be a commutative ring and let $M$ be an arbitrary $R$-module. In this talk, we will introduce the concept of strongly irreducible submodules of $M$ and we will prove some properties of them, whenever $M$ is either an arithmetical or a Noetherian module. In case when $R$ is Noetherian and $M$ is finitely generated, several characterizations of strongly irreducible submodules are included. Among other things, it is shown that when $N$ is a submodule of $M$ such that $N:_RM$ is not a prime ideal, then $N$ is strongly irreducible if and only if there exist a submodule $L$ of $M$ and a prime ideal $frak p$ of $R$ such that $N$ is $frak p$- ... |