WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS

Temel Bulgular & Veri:We also give some simple properties of this index and show that rings with the weakly nil-clean index 1 are precisely those rings that are abelian weakly nil-clean, thus showing that they coincide with uniquely weakly nil-clean rings.

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Sonuç & Katkı:Algebra 15(2014), 145–156]

🔬Tür:Araştırma Makalesi

📍Kapsam:2014 Verileri

⚙️Değişkenler:: Nil-clean ring · uniquely nil-clean ring · weakly nil-clean ring

Abstract

We introduce and study the weakly nil-clean index associated to a ring. We also give some simple properties of this index and show that rings with the weakly nil-clean index 1 are precisely those rings that are abelian weakly nil-clean, thus showing that they coincide with uniquely weakly nil-clean rings. Next, we define certain types of nilpotent elements and weakly nil-clean decompositions by obtaining some results when the weakly nil-clean index is at most 2 and, moreover, we somewhat characterize rings with weakly nil-clean index 2. After that, we compute the weakly nil-clean index for T2(Zp), T3(Zp) and M2(Z3), respectively, as well as we establish a result on the weakly nilclean index of Mn(R) whenever R is a ring. Our results considerably extend and correct the corresponding ones from [Int. Electron. J. Algebra 15(2014), 145–156]

Anahtar kelimeler

: Nil-clean ring uniquely nil-clean ring weakly nil-clean ring

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Bu Makaleye Atıf Yap

Ciımpean, A., Danchev, P. (2017). WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS. International Electronic Journal of Algebra, Cilt: 21 - Sayı: 21, 180–197. https://ajindex.com/articles/832366

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Kaynakça (11)

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