利用图的完形刻画wsr1条件

Characterizing wsr1 Condition by Completions of Diagrams

中文关键词:  wsr1条件  图完形  T-投影模

英文关键词:wsr1 condition  T-projectivity  completion of diagram

中文摘要:

      本文证明了：对于拟投射右R-模M，End_R（M）满足wsr1条件（即弱的stable range one条件）当且仅当M_R是T-投射模；wsr1条件是左右对称的;对于von Neumann正则环R，R满足wsr1条件当且仅当R为单侧幺正则环．

英文摘要:

      We prove that for a right quasi-projective R-module M, End_R (M) satisfies wsr1 condition if and only if M is a T-projective module. We prove that wsr1 condition is left-right symmetric. For von Neumann regular ring R, R satisfies wsr1 if and only if R is one-sided unit regular.