Asymptotic ideals (ideals in the ring of Colombeau generalized constants   with continuous parametrization)
  We study the asymptotics at zero of continuous functions on (0, 1] by means of their asymptotic ideals, i.e., ideals in the ring of continuous functions on (0, 1] satisfying a polynomial growth condition at 0 modulo rapidly decreasing functions at 0. As our main result, we characterize maximal and prime ideals in terms of maximal and prime filters. 
Anatole Khelif, Dimitris Scarpalezos and Hans Vernaeve
math.RA math.FA