Nil-clean matrix rings

We characterize the nil clean matrix rings over fields. As a by product, it is proved that the full matrix rings with coefficients in commutative nil-clean rings are nil-clean, and we obtain a complete characterization of the finite rank Abelian groups with nil clean endomorphism ring and the Abelia...

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Veröffentlicht in:arXiv.org 2013-10
Hauptverfasser: Breaz, S, Călugăreanu, G, Danchev, P, Micu, T
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Sprache:eng
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Zusammenfassung:We characterize the nil clean matrix rings over fields. As a by product, it is proved that the full matrix rings with coefficients in commutative nil-clean rings are nil-clean, and we obtain a complete characterization of the finite rank Abelian groups with nil clean endomorphism ring and the Abelian groups with strongly nil clean endomorphism ring, respectively.
ISSN:2331-8422