双边Artin环的一个刻划 |
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引用本文: | 杨士林.双边Artin环的一个刻划[J].北京工业大学学报,1996,22(3):85-87. |
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作者姓名: | 杨士林 |
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作者单位: | 北京工业大学计算机学院 |
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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≌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
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关 键 词: | 幂等元,除环,可逆元 |
A Characterization of Two-Sided Artinian Rings |
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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 T2 over Z2. |
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