Browsing by Subject "Projective-free ring"

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    Factorizations of matrices over projective-free Rings
    (World Scientific Publishing Co. Pte Ltd, 2016) Chen, H.; Kose, H.; Kurtulmaz, Y.
    An element of a ring R is called strongly J#-clean provided that it can be written as the sum of an idempotent and an element in J#(R) that commute. In this paper, we characterize the strong J#-cleanness of matrices over projective-free rings. This extends many known results on strongly clean matrices over commutative local rings. © 2016 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.
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    Sytongly P-clean Rings and Matrices
    (Elsevier, 2014) Chen, H.; Kose, H.; Kurtulmaz, Y.
    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.