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Mathematics of the USSR-Izvestiya, 1976, Volume 10, Issue 2, Pages 413–428
DOI: https://doi.org/10.1070/IM1976v010n02ABEH001701 (Mi im2118) 		 
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
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DOI: https://doi.org/10.1070/IM1976v010n02ABEH001701
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.
Received: 14.02.1974
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1976, Volume 40, Issue 2, Pages 433–447
Bibliographic databases:
UDC: 519.4
MSC: Primary 13E10, 13H05; Secondary 16A36, 32B10
Language: English
Original paper language: Russian
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/im2118}
\mathscinet{http://mathscinet.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}
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  • https://www.mathnet.ru/eng/im/v40/i2/p433
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:262
    Russian version PDF:72
    English version PDF:6
    References:40
    First page:2
     
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