| 郭学军,宋光天.APT环上幂等阵的对角化[J].数学研究及应用,2001,21(1):21~26 |
| APT环上幂等阵的对角化 |
| On Diagonalization of Idempotent Matrices over APT Rings |
| 投稿时间：1998-04-13 |
| DOI：10.3770/j.issn:1000-341X.2001.01.004 |
| 中文关键词: |
| 英文关键词:Abelian ring APT ring idempotent matrix. |
| 基金项目: |
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| 摘要点击次数: 2290 |
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| 中文摘要: |
| 设R是一阿贝尔环(R的所有幂等元都在中心里)，A是R上的一幂等阵.本文证明了以下结果：(a)A相抵于一对角阵当且仅当A相似于一对角阵；(b)若R是一APT(阿贝尔投射平凡)环，则A在相似变换之下可唯一地化为对角形diag{e1, ..., en｝，这里ei整除ei+1；(c)R是APT环当且仅当R/I是APT环，这里I是环R的一幂零理想.由(a)，还证明了分离的阿贝尔正则环是APT环. |
| 英文摘要: |
| Let R be an abelian ring ( all idempotents of R lie in the center of R), and A be an idempotent matrix over R. The following statements are proved: (a). A is equivalent to a diagonal matrix if and only if A is similar to a diagonal matrix. (b). If R is an APT (abelian projectively trivial) ring, then A can be uniquely diagonalized as diag{e1, ..., en} and ei divides ei+1. (c). R is an APT ring if and only if R/I is an APT ring, where I is a nilpotent ideal of R. By (a), we prove that a separative abelian regular ring is an APT ring. |
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