Von Neumann Regular and Related Elements in Commutative Rings

Let R be a commutative ring with nonzero identity. In this paper, we study the von Neumann regular elements of R. We also study the idempotent elements, …- regular elements, the von Neumann local elements, and the clean elements of R. Finally, we investigate the subgraphs of the zero-divisor graph i(R) of R induced by the above elements. 2000 Mathematics Subject Classiflcation: primary 13F99; secondary 16E50, 13A15