Faithful torsion rings and modules I

What is it about?

Given an R module M, if we postulate that the annihilator of M is nontrivial, the annihilator of each element is nontrivial. If instead we postulate that the annihilator of a single element is trivial, then the annihilator of M is trivial as well. In this article the authors explored the balance point of these two conditions: the annihilator of each element is nontrivial, and yet the annihilator of the entire module is trivial. The existence and minimum cardinalities of generating sets for such modules are considered.

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