The Mishnah (Kiddushin 3:12) states that, to be a Jew, one must be either the child of a Jewish mother or a convert to Judaism, (ger tzedek, “righteous convert”). This law originated in the Talmud (Kiddushin 68b). Orthodox opinion regards this rule as dating from receipt of the Torah at Mount Sinai, but most non-Orthodox scholars regard it as originating either at the time of Ezra (4th Century BCE) or during the period of Roman rule in the 1st2nd centuries CE
http://en.wikipedia.org/wiki/Matrilineality_in_Judaism
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