关键词: Radicaltotal 环, 分解, 总数, 幂等元

Abstract: The decomposition theorems on projective modules over radical total rings are built in this paper. For a total free ring $R$ with $u.{\rm dim}_{R}R < \infty$, it is showed that $R$ is Noetherian with gldim$R \leqslant 1$, and any projective module $P$ over $R$ is isomorphic to $ \bigoplus\limits_{i\in
I}Re_{i}$, in which each $e_{i}$ is a nonzero idempotent in $R$.
Some examples are also given.

Key words: Radicaltotal ring, Decomposition, Total, Idempotent