Duality and noncommutative planes

We study extensions of simple modules over an associative ring A   and we prove that for twosided ideals mm and nn with artinian factors the condition ExtA1(A/m,A/n)≠0 holds for the left A  -modules A/mA/m and A/nA/n if and only if it holds for the right modules A/nA/n and A/mA/m.The methods proving this are applied to show that noncommutative models of the plane, i.e. algebras of the form k〈x,y〉/(f)k〈x,y〉/(f), where f∈([x,y])f∈([x,y]) are noetherian only in case (f)=([x,y])(f)=([x,y]).