EMIS ELibM Electronic Journals Publications de l’Institut Mathématique, Nouvelle Série
Vol. 100[114], No. 1/1, pp. 287–298 (2016)

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Huanyin Chen, Sait Halicioglu, and Handan Kose

Department of Mathematics, Hangzhou Normal University, Hangzhou, China; Department of Mathematics, Ankara University, Ankara, Turkey; Department of Mathematics, Ahi Evran University, Kirsehir, Turkey

Abstract: An element a of a ring R is called perfectly clean if there exists an idempotent e 2 (a) such that a-eU(R). A ring R is perfectly clean in case every element in R is perfectly clean. In this paper, we completely determine when every 2×2 matrix and triangular matrix over local rings are perfectly clean. These give more explicit characterizations of strongly clean matrices over local rings. We also obtain several criteria for a triangular matrix to be perfectly J-clean. For instance, it is proved that for a commutative local ring R, every triangular matrix is perfectly J-clean in T n (R) if and only if R is strongly J-clean.

Keywords: perfectly clean ring; perfectly J-clean ring; quasipolar ring; matrix; triangular matrix

Classification (MSC2000): 16S50; 16S70; 16U99

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Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.

© 2016 Mathematical Institute of the Serbian Academy of Science and Arts
© 2016 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition