数学物理学报 ›› 2009, Vol. 29 ›› Issue (2): 378-382.

• 论文 • 上一篇    下一篇

关于置换环上强可分性的注记

  

  1. (杭州师范大学数学系 |杭州 310036)
  • 收稿日期:2007-12-27 修回日期:2008-11-20 出版日期:2009-04-25 发布日期:2009-04-25
  • 基金资助:

    杭州师范大学科研启动经费资助

A Note on Strongly Separativity over Exchange Rings

  1. (Department of Mathematics, Hangzhou Normal University, Hangzhou 310036)
  • Received:2007-12-27 Revised:2008-11-20 Online:2009-04-25 Published:2009-04-25
  • Supported by:

    杭州师范大学科研启动经费资助

摘要:

R是强可分的, 如果对任意有限生成投射R - 模A, B, A    A≌ B    B, 则A ≌ B. 该文证明了置换环上的强可分性在亚直积下是不变量. 作为应用, 证明了R/(IJ)是强可分的当且仅当R/(I∩J) 是强可分的.

关键词: 置换环, 强可分性, 直积

Abstract:

A ring R is strongly separative provided that, for any finitely generated projective right R-modules A and B, A    A ≌  A    B → A ≌ B. The author proves, in this note, that strongly separativity over exchange rings is invariant under subdirect products. As an application, the author proves that R/(IJ) is strongly separative if and only if so does R/(IJ) for any ideals of an exchange ring.

Key words: Exchange ring, Strong separativity, Direct product

中图分类号: 

  • 16D40