Is it ok to message an ex on Facebook

My ex broke up with me 13 years ago. We drifted apart, and it was amicable. My long time girlfriend/life partner (10 years) passed away a few months ago. We were never ones to be on social media, but I have recently set up an account and saw that my ex has an account. Is it ok to send her a message just as a friend to see how things are going? I have no idea of her relationship status and I am not looking to rekindle anything, just reaching out as a friend. Would this be weird? and if not, would I state in the message, I am not looking for anything so she doesn't get the wrong idea. Thanks

Sorry to her your partner passed away, there is reason you looked her up. Maybe you feel she is supportive? In my opinion it would not be weird, I’d start with hey, its been a long time I hope you are well and see how it goes. If she doesn’t reply then that’s fine too. I’m one for trying to follow my feeling about a situation. I wouldn’t even state your not looking for anything your both a lot older now and much has changed. Good luck

Thanks for the advice, appreciate it.