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Quasipolar property of trivial Morita context. (English) Zbl 1291.16022

Summary: Let \(T:=\left(\begin{smallmatrix} R&M\\ N&S\end{smallmatrix}\right)\) be a trivial Morita context. This article concerns the quasipolar properties of trivial Morita contexts over local rings. Necessary and sufficient conditions for a single matrix of \(T\) (a trivial Morita context over local rings) to be quasipolar are obtained. And then we get a sufficient condition for \(T\) to be a quasipolar ring.

MSC:

16S50 Endomorphism rings; matrix rings
16U80 Generalizations of commutativity (associative rings and algebras)
16L30 Noncommutative local and semilocal rings, perfect rings
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