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A ring R is called right closed semiregular if for every closed principal right ideal aR of R, there exists e2= e∈ aR such that (1− e) a∈ J (R). The class of right closed semiregular rings contains all semiregular rings and all right principally extending rings. Some properties of these rings are studied and some results about semiregular rings and right principally extending rings are extended.