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
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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.
@article{IM2_1976_10_2_a10,
author = {A. N. Shoshitaishvili},
title = {On the simplicity of the lattice of ideals of local rings of finite-to-one mappings of spaces of the same dimension},
journal = {Izvestiya. Mathematics },
pages = {413--428},
publisher = {mathdoc},
volume = {10},
number = {2},
year = {1976},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a10/}
}
TY - JOUR AU - A. N. Shoshitaishvili TI - On the simplicity of the lattice of ideals of local rings of finite-to-one mappings of spaces of the same dimension JO - Izvestiya. Mathematics PY - 1976 SP - 413 EP - 428 VL - 10 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a10/ LA - en ID - IM2_1976_10_2_a10 ER -
%0 Journal Article %A A. N. Shoshitaishvili %T On the simplicity of the lattice of ideals of local rings of finite-to-one mappings of spaces of the same dimension %J Izvestiya. Mathematics %D 1976 %P 413-428 %V 10 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a10/ %G en %F IM2_1976_10_2_a10
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/