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Let D be an integral domain and w be the so-called w-operation on D. We define D to be a w-FF domain if every w-flat w-ideal of D is of w-finite type. This paper presents some properties of w-FF domains and related domains. Among other things, we study the w-FF property in the polynomial extension, the t-Nagata ring and the pullback construction.

Integral Domains in Which Every Nonzero w-Flat Ideal Is w-Invertible