What is the ruling on women going out for shopping? And does this fall under the saying of Ali (may Allah be pleased with him): "Are you not jealous? You let your women go wherever they desire (to the markets)?"

For a woman to remain in her home is better for her, and this is what Allah has commanded in His saying: (And stay in your homes). A woman should not go out except out of necessity, and with her husband's permission, while adhering to the complete lawful hijab (definition). If she goes out displaying herself or wearing perfume, then that is not permissible for her. However, if there is no fear of temptation and she goes out in the manner required by Islamic law, there is no harm in it. Indeed, women used to go out during the time of the Prophet, peace and blessings be upon him, for their needs.