双边Artin环的一个刻划

设Ｒ是双边Ａｒｔｉｎ环，本文证明了若Ｒ的任意不可逆元均可表成Ｒ中幂等元的乘积，则Ｒ是下列３种情形之一的环：（１）Ｒ≌Ｍ＿ｎ（Ｄ）（ｎ≥１，Ｄ为某除环）。（２）Ｒ≌Ｚ＿２Ｚ＿２…Ｚ＿２（共ｓ个，ｓ≥２）。（３）Ｒ／Ｊ（Ｒ）≌Ｚ＿２Ｚ＿２．且Ｒ同构于Ｚ＿２上的上三角矩阵环Ｔ＿２

A Characterization of Two-Sided Artinian Rings

When R is a two-sided artinian ring, it is shown that if each non-invertible element of R can be expressed as a product of idempotents in R, then R satisfies one of the following:(1) R≌Mn (D) (n ≥1, D is some division ring)(2) R≌Z2 Z2 ... Z2(s copies, some s≥1).(3) R/J(R)≌ Z2 Z2, and R is an isostructrure of the upper triangular matrix ring T2 over Z2.