Can you get uterine cancer after removal of your ovaries?

Yes. Since the uterus is still present, cancer can develop in it. Additionally, even with ovaries removed, there are sometimes ovarian cells present that may lead to ovarian or "primary peritoneal" cancer from similar cells lining the abdominal cavity.
Depends. If your uterus was not removed then you can still get uterine cancer. If you still have your uterus you should continue to get pap smears.

Related Questions

If I had uterine cancer before and have a cyst on my ovary should I be scared. I don't have a uterus anymore?

What kind of cyst? I'm really glad you had a hysterectomy for your uterine cancer and trust that you'll have a good outcome. Most women have a cyst or two in the ovaries and if the radiologist isn't worried, I wouldn't be either. Best wishes.