Geodesic
Direct sums of distributive modules
Sbornik. Mathematics, Tome 187 (1996) no. 12, pp. 1869-1887 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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A. A. Tuganbaev. Direct sums of distributive modules. Sbornik. Mathematics, Tome 187 (1996) no. 12, pp. 1869-1887. http://geodesic.mathdoc.fr/item/SM_1996_187_12_a5/

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