Is it obligatory for a woman to greet men with "Salam," or is it impermissible because her voice is considered 'awrah? And are a woman's opportunities to accrue good deeds fewer than a man's?

Allah Almighty is the Disposer of affairs in the universe. Allah says: "It is not for a believing man or a believing woman, when Allah and His Messenger have decided a matter, that they should [thereafter] have any choice about their affair," and "But no, by your Lord, they will not [truly] believe until they make you, [O Muhammad], judge concerning that over which they dispute among themselves and then find within themselves no discomfort from what you have judged and submit in [full, willing] submission." It is permissible for a woman to greet men with peace (salaam) and vice versa, within legitimate Islamic guidelines, and a woman's voice is not considered 'awrah (that which must be covered or concealed) unless she softens her speech. As for the differences between the sexes and what has been ordained for men in some acts of worship, Allah compensates women for this if they maintain their homes and obey their husbands, making their obedience to him equivalent to striving in the cause of Allah (jihad). The fulfillment of instincts is shared, and every detail in the religion has been legislated for great wisdom and for the benefit of all.