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...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.展开更多
Some new rings are introduced, and their projective free properties are studied. Moreover, module structures of group rings are obtained, and Quillen-Suslin’s Theorem is generalized.
基金supported by NSFC(No.11471108)Natural Science Foundation of Hunan Province(Nos.2015JJ2051,2016JJ2050)+1 种基金Scientific Research Foundation of Hunan Provincial Education Department(No.12B101)the Teaching Reform Foundation of Hunan Province(No.G21316)
基金This research was supported by the Scientific and Technological Research Council of Turkey （2221 Visiting Scientists Fellowship Programme） and the Natural Science Foundation of Zhejiang Province （LY13A010019）, China.
文摘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.
文摘Some new rings are introduced, and their projective free properties are studied. Moreover, module structures of group rings are obtained, and Quillen-Suslin’s Theorem is generalized.
