On the simplicity of the lattice of ideals of local rings of finite-to-one mappings of spaces of the same dimension

In this paper we prove that the set of all ideals of a local ring which is a finite-dimensional $C$-algebra or $R$-algebra is canonically representable as a union of Grassmann varieties. We use this to determine the lattices of ideals of local rings of certain mappings. We give simple necessary and sufficient conditions for the simplicity of the lattice of ideals of the local ring of a finite-to-one mapping of spaces of the same dimension.
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