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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 6

First steps going down on algebraic frames

Themba Dube
Sayfa
1792–1807
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Namely, a commutative ring $A$ with identity is von Neumann regular if and only if $Ann(I)+P=A$, for every prime ideal $P$ of $A$ and any finitely generated ideal $I$ of $A$ contained in $P$.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We extend the ring-theoretic concept of going down to algebraic frames and coherent maps.
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Temel Bulgular & Veri:We then use the notion introduced to characterize algebraic frames of dimension 0 and frames of dimension at most 1.
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Sonuç & Katkı:Namely, a commutative ring $A$ with identity is von Neumann regular if and only if $Ann(I)+P=A$, for every prime ideal $P$ of $A$ and any finitely generated ideal $I$ of $A$ contained in $P$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Algebraic frame · Sublocale · Prime element

Abstract

We extend the ring-theoretic concept of going down to algebraic frames and coherent maps. We then use the notion introduced to characterize algebraic frames of dimension 0 and frames of dimension at most 1. An application to rings yields a characterization of von Neumann regular rings that appears to have hitherto been overlooked. Namely, a commutative ring $A$ with identity is von Neumann regular if and only if $Ann(I)+P=A$, for every prime ideal $P$ of $A$ and any finitely generated ideal $I$ of $A$ contained in $P$.

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Bu Makaleye Atıf Yap

Dube, T. (2022). First steps going down on algebraic frames. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 6, 1792–1807. https://ajindex.com/articles/529762

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Kaynakça (17)

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