• The group of invertible ideals of a Prüfer ring

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/130/0011

• # Keywords

Prüfer ring; invertible ideals; $H$-local ring; Marot ring; weakly additively regular ring

• # Abstract

Let $R$ be a commutative ring and $\mathcal{I}(R)$ denote the multiplicative group of all invertible fractional ideals of $R$, ordered by $A \leq B$ if and only if $B \subseteq A$. We investigate when there is an order homomorphism from $\mathcal{I}(R)$ into the cardinal direct sum $\coprod_{i\in I} G_{i}$, where $G_{i}$ ’s are value groups, if $R$ is a Marot Prüfer ring of finite character. Furthermore, over Prüfer rings with zero-divisors, we investigate the conditions that make this monomorphism onto.

• # Author Affiliations

1. Department of Mathematics, Izmir Institute of Technology, Izmir, Turkey

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019