Recent content by frankusho

A left Artinian ring R is a ring for which every descending chain R=I0 ⊃I1 ⊃I2 ⊃…⊃In ⊃… of its left ideals stabilizes, i.e. there is a k such that In+1 =In for all n≥k A right Noetherian ring R is ring in which every ascending chain of right ideals stabalizes

A left deal I of a ring R is left nilpotent if there is a positive integer n > 0 such that In=0 A nil left ideal is a left ideal in which every element is nilpotent, i.e. for all i in I there exists a n>0such that in=0

1. Prove that a ring which is left Artinian and right Noetherian is right Artinian. The Attempt at a Solution I can't figure it out. Can anyone help?

1. Show that the sum of a nilpotent left ideal and a nil left ideal is a nil left ideal. 2. The attempt at a solution So far, I have no idea where to begin.