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Nilpotency for Morita context rings. (Chinese. English summary) Zbl 1129.16300

Summary: Let \((A,B,V,W,(\,),[\,])\) be a Morita context and \(C=\left(\begin{smallmatrix} A&V\\ W&B\end{smallmatrix}\right)\) the corresponding Morita context ring. Using basic methods in ring theory, the authors present some properties between \(C\) and \(A,B,V,W\) on nilness, nilpotency, local nilpotency, \(N\)-nilness and \(P\)-property.

MSC:

16D90 Module categories in associative algebras
16N40 Nil and nilpotent radicals, sets, ideals, associative rings
16S50 Endomorphism rings; matrix rings
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