Geodesic
Pure Simple and Indecomposable Rings
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 71-78

Voir la notice de l'article provenant de la source Cambridge University Press

P. M. Cohn [7] calls a submodule P of the left A-module M pure iff 0 → E ⊗ P → E ⊗ M is exact for all right modules E. This concept has been studied in [11] and [12]. We will call a non-zero module pure simple iff its only pure submodules are 0 and itself, and the ring A left pure simple iff it is pure simple as a left A-module. We relate these concepts to the PP and PF rings of Hattori [13], and give several new characterizations of these rings. In order to establish these, we use the following known result: the Jacobson radical of any module is the sum of all its small submodules.Parts of this paper are contained in the author's doctoral thesis [10] at McGill University. 
Fieldhouse, David J. Pure Simple and Indecomposable Rings. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 71-78. doi: 10.4153/CMB-1970-015-4
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