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Why does it say that she heard of the death of her Ish, and eulogized her Ba'al?
1.
Malbim: Ish alludes to the love between them. Ba'al alludes to that he had Bi'ah with her, or his authority over her. They told her that her Ish died - they thought that they are still lovers. She eulogized her Ba'al, for she was divorced. 1
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He divorced her amidst love, lest she be Agunah afterwards! Perhaps she ceased to love him, for she understood that David wants to marry her, and she desired him more than Uriyah. (PF)