✨
AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Moreover, we investigate the (weak) quasi regular property of trivial extension.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:Recall that a ring $R\ $is said to be a quasi regular ring if its total quotient ring $q(R)\ $is \textit{von Neumann regular}.
📊
Key Findings & Data:It is well known that a ring $R\ $is quasi regular if and only if it is a reduced ring satisfying the property: for each $a\in R,$ $ann_{R}(ann_{R}(a))=ann_{R}(b)$ for some $b\in R$.
💡
Conclusion & Impact:Moreover, we investigate the (weak) quasi regular property of trivial extension.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:von Neumann regular rings · quasi regular rings · von Neumann regular module
Abstract
Recall that a ring $R\ $is said to be a quasi regular ring if its total quotient ring $q(R)\ $is \textit{von Neumann regular}. It is well known that a ring $R\ $is quasi regular if and only if it is a reduced ring satisfying the property: for each $a\in R,$ $ann_{R}(ann_{R}(a))=ann_{R}(b)$ for some $b\in R$. Here, in this study, we extend the notion of quasi regular rings and rings which satisfy the aforementioned property to modules. We give many characterizations and properties of these two classes of modules. Moreover, we investigate the (weak) quasi regular property of trivial extension.
Keywords
🔖
Cite This Article
Jayaram, C., Tekir, Ü., Koç, S. (2021). Quasi regular modules and trivial extension. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 1. https://doi.org/10.15672/hujms.613404