Duality and noncommutative planes

• Søren Jøndrup ^[1]
  1. [1] University of Copenhagen

     University of Copenhagen

     Dinamarca

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 3 ((March 2015)), 2015 (Ejemplar dedicado a: Special Issue in honor of Prof. Hans-Bjørn Foxby), págs. 563-568
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.05.014
• Enlaces
  • Texto completo
• Resumen

  • 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]).