Geodesic
On the simplicity of the lattice of ideals of local rings of finite-to-one mappings of spaces of the same dimension
Izvestiya. Mathematics, Tome 10 (1976) no. 2, pp. 413-428 
A. N. Shoshitaishvili. On the simplicity of the lattice of ideals of local rings of finite-to-one mappings of spaces of the same dimension. Izvestiya. Mathematics, Tome 10 (1976) no. 2, pp. 413-428. http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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. Bibliography: 6 titles.

[1] Atya M., Makdonald I., Vvedenie v kommutativnuyu algebru, Mir, M., 1972 | MR

[2] Birkgof G., Teoriya struktur, IL, M., 1952

[3] Arnold V. I., “Osobennosti gladkikh otobrazhenii”, Uspekhi matem. nauk, 23:1(139) (1968), 3–44 | MR

[4] Mazer D. N., “Ustoichivost $C^\infty$-otobrazhenii. III. Konechnaya opredelennost rostkov otobrazhenii”, Matematika, 14:1 (1970), 146–175

[5] Kertis Ch., Rainer I., Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969 | MR

[6] Shoshitaishvili A. N., “Struktura idealov lokalnykh kolets konechnokratnykh otobrazhenii prostranstv odinakovoi razmernosti dvoistvenna samoi sebe”, Uspekhi matem. nauk, 29:3(177) (1974), 237–238 | MR