1-SEPARABLE TORSION FREE MODULES OVER INTEGRAL DOMAINS
Keywords:
torsion free module, integral domain, separable module, quasi-isomorphism, torsion free abelian groupDOI:
https://doi.org/10.17654/0972555522035Abstract
A torsion free module over an integral domain is called separable (resp. 1-separable) if every finite subset of elements (resp. each element) is contained in a completely decomposable direct summand. In this work, it is shown that over an integral domain, a 1-separable module M is separable in case each homogeneous direct summand of finite rank in M has the property that its pure rank 1 submodules are direct summands.
Received: July 27, 2022
Revised: October 14, 2022
Accepted: October 18, 2022
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