Sytongly P-clean Rings and Matrices
Journal of Algebra and its Applications
116 - 131
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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.
KeywordsStrongly P-clean ring
Uniquely nil-clean ring