Abstract
Let [Formula: see text] be a commutative ring with identity. The purpose of this paper is to introduce and to study a new class of modules over [Formula: see text] called quasi-primaryful [Formula: see text]-modules. This class contains the family of finitely generated modules properly, on the other hand it is contained in the family of primeful [Formula: see text]-modules properly, and three concepts coincide if they are multiplication modules. We show that free modules, projective modules over domains and faithful projective modules over Noetherian rings are quasi-primaryful modules. In particular, if [Formula: see text] is an Artinian ring, then all [Formula: see text]-modules are quasi-primaryful and the converse is also true when [Formula: see text] is a Noetherian ring.
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