Abstract
Let [Formula: see text] be a regular ideal in noetherian ring [Formula: see text]. Mc Adam and Ratliff showed the existence of the unique minimal reduction number of [Formula: see text], noted [Formula: see text], such that for every minimal reduction [Formula: see text] of [Formula: see text], [Formula: see text] and [Formula: see text]. They showed that the set of integers [Formula: see text] is bounded in terms of the analytic spread of [Formula: see text]. Here, we extend these results to good filtrations. Let [Formula: see text] be a good filtration on [Formula: see text], we show that the set of integers [Formula: see text] is bounded.
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