Right Noetherian domain
= Right Noetherian domain
A <noncommutative domain> whose <right ideals> satisfy the <ascending chain condition> is a right Noetherian domain. Its right regular <module> is a <uniform module>, so any two nonzero principal <right ideals> intersect. Thus its nonzero elements satisfy the <right Ore condition> and it embeds in a <division ring> by <Ore localization>.