We prove that the property Add (M) Prod (M) characterizes sigma-algebraically compact modules if |M| is not -measurable. Moreover, under a large cardinal assumption, we show that over any ring R where |R| is not -measurable, any free module M of -measurable rank satisfies Add (M) Prod (M), hence the assumption on |M| cannot be dropped in general (e.g., over small non-right perfect rings). In this way, we extend results from arecent paper by Simion Breaz .
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机译：我们证明如果| M |，则属性Add（M）Prod（M）表示sigma-代数紧凑模块。是不可衡量的。而且，在大的基本假设下，我们表明在任何环R上，| R |是不可测量的，可测量等级的任何自由模块M都满足加（M）Prod（M），因此| M |的假设一般不能掉落（例如，在不正确的小型完美环上）。这样，我们扩展了Simion Breaz的最新论文的结果。
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