Mathergavethenecessaryandsufficientconditionsforthefinitedeterminacys-moothfunctiongermswithnomorethancodimension4.Thetheoremisveryeffectiveondetermininglowcodimensionsmoothfunctiongerms.Inthispaper,theconceptofrightequivalentforsmoothfunctiongermsringgeneratedbytwoidealsfinitelyisdefined.Thecontainmentrelationshipsoffunctiongermsstillsatisfyfinitek-determinacyundersufficientlysmalldisturbancewhicharediscussedinorbittangentspaces.Furthermore,themethodsinjudgingtherightequivalencyofArnoldfunctionfamilywithcodimension5arepresented.