maximal right ideal meaning in English

极大右理想

The first chapter , main instead " duo - ring " condition of " every maximal left ideal is gw - ideal " condition , study strongly regularities of gp - v - ring on this condition . lt is shown that ( 1 ) r is strongly regular iff r is left gp - v - ring whose maximal left ideals are gw - ideal . ( 2 ) r is strongly regular iff r is left gp - v - ring whose maximal right ideals are gw - ideal . the second chapter , generalize some results of gp - v - ring to gp - v - ring , discuss regularity of gp - v ' - ring . it is shown that ( 1 ) r is left self - injective regular with non - zero socle iff r is left gp - v - ring with soc ( rr ) = soc ( rr ) and r contains an injective maximal left ideal
第一章主要将“ duo -环”条件替换成“每一极大左(右)理想是gw -理想”条件，研究在此条件下， gp - v -环的强正则性，证明了： ( 1 ) r是强正则环当且仅当r是左gp - v -环且r的每一极大左理想是广义弱理想； ( 2 ) r是强正则环当且仅当r是左gp - v -环且r的每一极大右理想是广义弱理想，第二章，主要将gp - v -环上一些结果推广到gp - v -环上，讨论gp - v -环的正则性，证明了： ( 1 ) r是左自内射正则环且soc ( _ rr ) 0当且仅当r是包含内射极大左理想的gp - v -环，且soc ( _ rr ) = soc ( r _ r ) ； ( 2 ) r是正则环且每一极大本质左理想是理想当且仅当r是左gp -内射的左gp - v -环且每一极大本质左理想是理想。