Semiclean Rings

The notion of semiclean elements in a ring is defined. Every clean element is semiclean. A ring R is said to be semiclean if every element in R is semiclean. The group ring Z_pG with G a cyclic group of order 3 is proved to be semiclean. The n × n matrix ring M_n(R) over a semiclean ring is semiclean. If R is a torsion free semiclean ring in which every element of R can be written as a sum of periodic and ±1, then R is clean. Every element in a semiclean ring R with 2 invertible is a sum of no more than 3 units.