On Diagonalization of Idempotent Matrices over APT Rings
Received:April 13, 1998  
Key Words: Abelian ring   APT ring   idempotent matrix.  
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Author NameAffiliation
GUO Xue-jun Dept. of Math., University of Science and Technology of China, Heifei 230026, China 
SONG Guang-tian Dept. of Math., University of Science and Technology of China, Heifei 230026, China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.2001.01.004
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