ascending chain condition in a sentence

Examples

1. ;"'Noetherian ring "': A ring satisfying the ascending chain condition for left ideals is " left Noetherian "; a ring satisfying the ascending chain condition for right ideals is " right Noetherian "; a ring that is both left and right Noetherian is " Noetherian ".
2. ;"'Noetherian ring "': A ring satisfying the ascending chain condition for left ideals is " left Noetherian "; a ring satisfying the ascending chain condition for right ideals is " right Noetherian "; a ring that is both left and right Noetherian is " Noetherian ".