(Mishnah): [Women die...] because they are not careful about Nidah, Chalah, and lighting Ner [Shabbos].

Adam ha'Rishon was the blood (Nefesh) of the world - "v'Ed Ya'aleh Min ha'Aretz'', and Chavah caused death to him. Therefore, the Mitzvah of Nidah was given to woman.

[Chalah] was given to woman, for Adam ha'Rishon was Chalah Tehorah for the world - "va'Yitzer Hash-m Elokim Es ha'Adam Afar Min ha'Adamah'' (he was taken from the earth, just like Chalah is taken from dough);

This is like R. Yosi bar Ketzirtah taught, that once a woman wets her dough in water, she takes off its Chalah.

Chavah caused death to him, therefore, the Mitzvah of Chalah was given to woman.

And lighting Ner [Shabbos] - Adam ha'Rishon was the lamp of the world - "Ner Elokim Nishmas Adam'', and Chavah caused death to him. Therefore, the Mitzvah of Ner was given to woman.

(Beraisa - R. Yosi): Three things make death come prematurely (if one is not careful about them), and all three of them were given to woman. They are the Mitzvos of Nidah, Chalah and lighting.