Do Sheitels Still Have an Avoda Zara Problem? 3 Books Address the Issue

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I recommend you study them in the above order and come to your own conclusions.

(And then there is the question of whether such a hair-covering is even halachically effective for a married woman in Reshus Harabim at all. For that one, read this: קונטרס בענין כיסוי השיער.)