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Mat. Sb., 1996, Volume 187, Number 12, Pages 137–156 (Mi msb181)  

This article is cited in 2 scientific papers (total in 2 papers)

Direct sums of distributive modules

A. A. Tuganbaev

Moscow Power Engineering Institute (Technical University)

Abstract: A module is said to be distributive if the lattice of all its submodules is distributive. A direct sum of distributive modules is called a semidistributive module. It is proved that the prime radical of the ring of endomorphisms of a finite direct sum of distributive modules contains all one-sided nilideals of the ring of endomorphisms of this module. A semiprime ring with the maximal condition for right annihilators that decomposes into a direct sum of distributive right ideals is a finite direct product of prime rings.

DOI: https://doi.org/10.4213/sm181

Full text: PDF file (295 kB)
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English version:
Sbornik: Mathematics, 1996, 187:12, 1869–1887

Bibliographic databases:

UDC: 512.55
MSC: Primary 16D70, 16D80; Secondary 16S50, 16P60, 16P40, 06D99
Received: 23.01.1996

Citation: A. A. Tuganbaev, “Direct sums of distributive modules”, Mat. Sb., 187:12 (1996), 137–156; Sb. Math., 187:12 (1996), 1869–1887

Citation in format AMSBIB
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\paper Direct sums of distributive modules
\jour Mat. Sb.
\yr 1996
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\issue 12
\pages 137--156
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\transl
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\yr 1996
\vol 187
\issue 12
\pages 1869--1887
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Tuganbaev, “Semidistributive hereditary rings”, Russian Math. Surveys, 52:4 (1997), 848–849  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. A. A. Tuganbaev, “Semidistributive and distributively decomposable rings”, Math. Notes, 65:2 (1999), 253–258  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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