What is the immigration status of a women married to a divorcee who is a citizen of US

You need to apply for a green card and follow immigration procedures for applying.

No one is this country is entitled to US citizenship "automatically" but people who are born in the USA; born outside of the USA to a US citizen parents or, in some situations, USC parent, or otherwise derived citizenship by operation of law. Spouses of USCs do not fall in any of these categories. Hence, you will have to file the I-130 immigrant petition for your spouse like everyone else. That is regardless of whether you are divorced or never been married before. AS long as your current marriage is valid - which would require you be divorced from all your prior spouses first - and you are not disqualified by the Adam WAlsh Act, you can petition for your spouse and you will have to do that if you want the spouse to become an LPR.

You will need to file a petition for your wife. She will either have to consular process or adjust status to obtain a green card. Within 3 years she may then be eligible to file for citizenship depending on her particulars. Everyone who is not born here has to file to obtain some status. Marriage to a U. S. citizen does not give any automatic rights.

If your spouse is here, then you file an adjustment of status packet and - in the bay area - you are looking at about 4 months before your spouse gets a green card as long as there are no "admissibility" issues. If your spouse is outside the country, it is a slower, two stage process that will take about a year.

Your wife is eligible for immigration benefits, but you have to petition and sponsor her residency.

You need to petition for her status. If she is in the U.S. then she may also apply for adjustment of status based on that petition. This does not happen automatically.

There's no such thing as ebing "automatically eligible" for a Green Card and there's no such thing as being automatically eligible for U.S. Citizenship unless you are a natural born citizen as described in 8 USC 1401. You have to apply for an I-130 as the Petitioner and an I-485 for your wife to adjust status. This is a long process and you should hire a lawyer for this. Green card benefits are privileges and they bestow no "rights" under the Constitution as it pertains to immigration matters. That means USCIS is free to accept or reject it if they suspect marriage fraud or that it is not a bona fide marriage and there's really nothing you cao do except appeal it to the Board of immigration Appeals. SO you have to do a eptition for alien relative and an adjustment of status for her to obtaint her privilege of a greenc ard by being married to a US Citizen.