right regular ring 中文意思是什麼
right regular ring
解釋
右正則環-
2 ) let r is a semiprime ring, if r is a left sf - ring whose every special right annihilator is w - ideal, then r is a strongly regular ring
2 ）設r是半素環，如果r是左sf -環且r的每個特殊右零化子是w -理想，則r是強正則環。 -
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
第一章主要將「 duo -環」條件替換成「每一極大左（右）理想是gw -理想」條件，研究在此條件下， gp - v -環的強正則性，證明了： （ 1 ） r是強正則環當且僅當r是左gp - v -環且r的每一極大左理想是廣義弱理想； （ 2 ） r是強正則環當且僅當r是左gp - v -環且r的每一極大右理想是廣義弱理想，第二章，主要將gp - v -環上一些結果推廣到gp - v -環上，討論gp - v -環的正則性，證明了： （ 1 ） r是左自內射正則環且soc （ _ rr ） 0當且僅當r是包含內射極大左理想的gp - v -環，且soc （ _ rr ） = soc （ r _ r ） ； （ 2 ） r是正則環且每一極大本質左理想是理想當且僅當r是左gp -內射的左gp - v -環且每一極大本質左理想是理想。
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