Finite determinacy relative to closed and finitely generated ideals (Q1592850)

The main purpose of this paper is to develop a theory of finite determinacy and unfolding for \({\mathcal C}^\infty\)-function germs in a finitely generated and closed ideal with three additional hypotheses denoted by \((H_1) -(H_3)\). Some particular interesting situations have been studied by \textit{D. Siersma} [Proc. Symp. Pure Math. 40, part 2, 4855-496 (1983; Zbl 0514.32007)], \textit{R. Pellikaan} [Proc. Lond. Math. Soc. (3) 57, No. 2, 357-382 (1988; Zbl 0621.32019)], and \textit{G. Jiang} [Functions with nonisolated singularities on singular spaces. Thesis, Universiteit Utrecht (1988)].