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It is well known that for an integral domain A, the property that a module is divisible if and only if it is injective is equivalent to the property that A is a Dedekind domain. In this paper, it is shown that if A is a left Ore domain, then a torsion-free left A -module is divisible if and only if it is injective.doi:10.1090/s0002-9939-1970-0257155-2 fatcat:cbutz7gpyveylgfu42eqiepldq