  Kurihara established a refinement of the minus-part of the Iwasawa main
conjecture for totally real number fields using the higher Fitting ideals. In
this paper, by using Kurihara's methods and Mazur-Rubin theory, we study the
higher Fitting ideals of the plus-part of Iwasawa modules associated the
cyclotomic Z_p-extension of abelian fields for an odd prime number p. We define
the higher cyclotomic ideals C_i for any non-negative integer i, which are
ideals of the Iwasawa algebra defined by the Kolyvagin derivative classes of
circular units, and prove that they give upper and lower bounds of the higher
Fitting ideals in some sense, and determine the pseudo-isomorphism classes of
the plus-part of Iwasawa modules. Our result can be regarded as an partial
analogue of Kurihara's results and a refinement of the plus-part of the Iwasawa
main conjecture for abelian fields.
