The scholars differed concerning the ruling on offering the udhiyah: is it obligatory, such that the one who does not do it is sinning, or is it a confirmed Sunnah, such that it is makrooh (disliked) not to do it? The correct view is that it is a confirmed Sunnah (sunnah mu’akkadah). This has been discussed previously in the answer to question no. 36432
In order for it to be obligatory or Sunnah to offer the udhiyah, it is stipulated that the one who offers it should be independent of means, in that the price of the udhiyah is surplus to his needs and the needs of those on whom he spends. If a Muslim has a salary that comes to him every month, and this salary is sufficient for him and he has surplus money which which he can afford the price of the udhiyah, then in his case it is prescribed for him to offer the udhiyah.
The fact that it is stipulated that he should be independent of means is indicated by the words of the Prophet (blessings and peace of Allah be upon him): “Whoever can afford it but does not offer a sacrifice, let him not come near our prayer-place.” Narrated by Ibn Maajah, 3123; classed as hasan by al-Albaani in Saheeh Ibn Maajah. What is meant by being able to afford it is being independent of means.
The udhiyah is prescribed for the members of the household, because the Prophet (blessings and peace of Allah be upon him) said: “The people of each household should offer an udhiyah every year.” Narrated by Ahmad, 20207. Al-Haafiz Ibn Hajar said in Fath al-Baari: Its isnaad is qawiy. It was classed as hasan by al-Albaani in Saheeh Sunan Abi Dawood, 2788.
There is no difference between men and women in this regard. If a woman is living on her own or with her children, then they should offer the udhiyah.
It says in al-Mawsoo‘ah al-Fiqhiyyah (5/81):
Being male is not a condition of it being obligatory or sunnah to offer the udhiyah; as it is required of males it is also required of females, because the evidence for it being obligatory or Sunnah applies to everyone.
End quote. See: al-Majmoo‘ah al-Fiqhiyyah, 5/79-81
And Allah knows best.