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ON HOLLOW-WEAK LIFTING MODULES | ||
| Journal of Al-Nahrain University - Science | ||
| Article 1, Volume 13, Issue 1, 2010, Pages 157-159 | ||
| Author | ||
| Sahira M.Yaseen | ||
| Abstract | ||
| Let R be any ring and let M be any right R-module. M is called hollow-weak lifting if every semisimple submodule N of M such that M/N is hollow has a cossential submodule that is a direct submmand of M. We prove that M is hollow-weak lifting iff every semisimple N of M such that M/N is hollow has strong supplemented in M.And show that M is hollow-weak lifting iff every semisimple submodule N of M such that M/N is hollow can be written as N=KÅL with K is direct summand of M and L is small submodule of M. | ||
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