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 Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 2, Pages 433–447 (Mi izv2118)

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

A. N. Shoshitaishvili

Abstract: 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.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:2, 413–428

Bibliographic databases:

UDC: 519.4
MSC: Primary 13E10, 13H05; Secondary 16A36, 32B10

Citation: 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”, Izv. Akad. Nauk SSSR Ser. Mat., 40:2 (1976), 433–447; Math. USSR-Izv., 10:2 (1976), 413–428

Citation in format AMSBIB
\Bibitem{Sho76} \by A.~N.~Shoshitaishvili \paper On the simplicity of the lattice of ideals of local rings of finite-to-one mappings of spaces of the same dimension \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1976 \vol 40 \issue 2 \pages 433--447 \mathnet{http://mi.mathnet.ru/izv2118} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=409460} \zmath{https://zbmath.org/?q=an:0348.13002} \transl \jour Math. USSR-Izv. \yr 1976 \vol 10 \issue 2 \pages 413--428 \crossref{https://doi.org/10.1070/IM1976v010n02ABEH001701}