• The group of invertible ideals of a Prüfer ring

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      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

       

      BASAK AY SAYLAM1

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

       
  • Proceedings – Mathematical Sciences | News

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