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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
Similar characterization is obtained for T3(R) over a weak h-ring R.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:A ring R is strongly clean provided that for any a ∈ R, there exist an idempotent e ∈ R and a unit u ∈ R such that a = e + u and eu = ue.
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Temel Bulgular & Veri:Let T3(R) be a special subring of 3 by 3 matrix ring over R.
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Sonuç & Katkı:Similar characterization is obtained for T3(R) over a weak h-ring R.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:strongly clean ring · matrix ring · local ring
Abstract
A ring R is strongly clean provided that for any a ∈ R, there exist an idempotent e ∈ R and a unit u ∈ R such that a = e + u and eu = ue. Let T3(R) be a special subring of 3 by 3 matrix ring over R. We prove, in this article, that T3(R) is strongly clean if and only if for any a ∈ J(R), b ∈ R, c ∈ 1 + J(R), either lb − ra or lb − rc is surjective. Similar characterization is obtained for T3(R) over a weak h-ring R.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
Chen, H. (2011). A NOTE ON STRONGLY CLEAN MATRICES. International Electronic Journal of Algebra, Cilt: 10 - Sayı: 10, 192–204. https://ajindex.com/articles/832490