Abstract
A module M is called mathfrak {s}-coseparable if for every nonzero submodule U of M such that M/U is finitely generated, there exists a nonzero direct summand V of M such that V subseteq U and M/V is finitely generated. It is shown that every non-finitely generated free module is mathfrak {s}-coseparable but a finitely generated free module is not, in general, mathfrak {s}-coseparable. We prove that the class of mathfrak {s}-coseparable modules over a right noetherian ring is closed under finite direct sums. We show that the class of commutative rings R for which every cyclic R-module is mathfrak {s}-coseparable is exactly that of von Neumann regular rings. Some examples of modules M for which every direct summand of M is mathfrak {s}-coseparable are provided.
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