%0 Journal Article
%A LI Ai-Hua
%A LI Qi-Sheng
%T Quas i- dual Bimodules and Dual Rings
%D 2001
%R
%J Journal of Jishou University(Natural Sciences Edition)
%P 86-88
%V 22
%N 4
%X In this paper, left quasi- dual bimodules can be charac terized as those bimodules for which any submodule K of *M*_{R} and any left idea L of _{S}S are a direct summand of rM *l*_{S} (K ) and *l*_{S} *r*_{M} ( L ) respectly. For a left quasi- dual bimodule _{S}M_{R}, some results are proved: ( 1) _{S}M is a Kasch module, ( 2) *r*_{M} l_{S} ( Soc( *M*_{R} ) ) = Soc(*M*_{R} ) and *l*_{S} r_{M} ( Soc( _{S}S ) ) = Soc( _{S}S ) , ( 3) *l*_{S}( Soc( *M*_{R} ) ) *J ( S)* and *r*_{M} ( Soc( _{S}S ) ) Rad( *M*_{R} ) , ( 4) if *M*_{R} is a CS- module, the Soc

( *M*_{R} ) _{e}M_{R} , ( 5) if *M*_{R} is nonsingular, then *M* is semisimple, ( 6) if *M*_{R} is project ive in [* M*] and *M*_{R} is semisimple, the *M* is a nonsingular module. It deduced that if *R* is a left dualring or a left quasi- dual ring, then *R* is a semisimple if *R* is nonsingular.
%U https://zkxb.jsu.edu.cn/EN/abstract/article_1370.shtml