Chen, H.Kose, H.Kurtulmaz, Y.2015-07-282015-07-2820140024-3795http://hdl.handle.net/11693/12587Abstract. 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.EnglishStrongly P-clean ringn×n matrixProjective-free ringUniquely nil-clean ring16S5016U99Boolean ringArticle10.24330/ieja.2662421873-1856