Idempotent elements in an R0 algebra and it′s applications are studied. The concepts of idempotent element, left map and idempotent map are introduced in an R0 algebra. The characterizations of idempotent elements are discussed and it′s proved that the set of all idempotent elements in an R0 algebra is the biggest Boole algebra among all sub-algebras. Moreover, the left maps constructed by idempotent elements are idempotent maps. Using these results, a decomposition theorem of an R0 algebra is proved, which says that an R0 algebra can be decomposed as the direct production of the image and kernel of the idempotent map induced by idempotent elements.

R0 algebra; idempotent element; left map; idempotent map; direct production; kernel of a map