SOME CLASSES OF 2-GOOD RINGS

‎A ring R is said to be clean if every element of R is‎ ‎a sum of an idempotent and a unit‎. ‎A ring R is a neat‎ ‎ring if every nontrivial homomorphic image is clean‎. ‎In this‎ ‎paper first we prove that a neat ring is 2-good if no factor ring of R is isomorphic to Z_2 then by‎ ‎considering the structure of FGC rings we could prove that FGC rings are 2-good‎. ‎Finally by a counterexample we‎ ‎conclude that Be zout rings may‎ ‎not be 2-good‎.