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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
Moreover, we investigate the (weak) quasi regular property of trivial extension.
📌 3 Maddede Bu Makale
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Amaç & Hipotez: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}.
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Temel Bulgular & Veri: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 $b\in R$.
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Sonuç & Katkı:Moreover, we investigate the (weak) quasi regular property of trivial extension.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
Jayaram, C., Tekir, Ü., Koç, S. (2022). Quasi regular modules and trivial extension. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 1, 120–134. https://ajindex.com/articles/529455