Geodesic
On Modules of Singular Submodule Zero
Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 345-354

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

In this paper we generalize to modules of singular submodule zero over a ring of singular ideal zero some of the results, which are well known for torsion-free modules over a commutative integral domain, e.g. [2, Chapter VII, p. 127], or over a ring, which possesses a classical right quotient ring, e.g. [13, § 5].Let R be an associative ring with 1 and let M be a unitary right R-module, the latter fact denoted by MR . A submodule NR of MR is large in MR (MR is an essential extension of NR ) if NR intersects non-trivially every non-zero submodule of MR; the notation NR ⊆′ MR is used for the statement “NR is large in MR” The singular submodule of MR, denoted Z(MR ), is then defined to be the set {m ∈ M| r(m) ⊆’ RR}, where 
Cateforis, Vasily C.; Sandomierski, Francis L. On Modules of Singular Submodule Zero. Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 345-354. doi: 10.4153/CJM-1971-035-0
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