Duality and noncommutative planes

We study extensions of simple modules over an associative ring A and we prove that for twosided ideals m and n with artinian factors the condition Ext(A)(1)(A/m, A/n) not equal 0 holds for the left A-modules A/m and A/n if and only if it holds for the right modules A/n and A/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), where f is an element of([x,y]) are noetherian only in case (f) = ([x,y]).(C) 2014 Elsevier B.V. All rights reserved.