Algebras in which every subalgebra is noetherian
  We show that the twisted homogeneous coordinate rings of elliptic curves by infinite order automorphisms have the curious property that every subalgebra is both finitely generated and noetherian. As a consequence, we show that a localisation of a generic Skylanin algebra has the same property. 
D. Rogalski, S. J. Sierra, J. T. Stafford
math.RA