双边Artin环的一个刻划
A Characterization of Two-Sided Artinian Rings
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摘要: 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≌Mn(D)(n≥1,D为某除环).
(2)R≌Z2⊕Z2⊕…⊕Z2(共s个,s≥2).
(3)R/J(R)≌Z2⊕Z2.且R同构于Z2上的上三角矩阵环T2.Abstract: 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 T22 over Z2.
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