STRONGLY P-CLEAN RINGS AND MATRICES

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International Electronic Journal of Algebra
Volume:15 Issue:15
STRONGLY P-CLEAN RINGS AND MATRICES

STRONGLY P-CLEAN RINGS AND MATRICES

Authors : Huanyin CHEN, Handan KÖSE, Yosum KURTULMAZ

Pages : 116-131

Doi:10.24330/ieja.266242

View : 16 | Download : 12

Publication Date : 2014-06-01

Article Type : Research Paper

Abstract :An element of a ring R is strongly P-clean provided that it can be written as the sum of an idempotent and a strongly nilpotent element that commute. A ring R is strongly P-clean in case each of its elements is strongly P-clean. We investigate, in this article, the necessary and sufficient conditions under which a ring R is strongly P-clean. Many characterizations of such rings are obtained. The criteria on strong P-cleanness of 2 × 2 matrices over commutative projective-free rings are also determined.
Keywords : Strongly P clean ring, n×n matrix, projective free ring, uniquely nil clean ring, Boolean ring

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