Can I carry my dog's ashes onto an airplane with me?

Can I carry my dogs ashes onto an airplane with me?
She was the best thing in my life while she was alive and I just PERSONALLY want more than any other item in my possession to make sure her ashes stay with me at all times when I'm moving. I heard so many things about ashes being moved and I'm just concerned. I also worry they might check to make sure it's not drugs or something and then desecrate her ash box! Anyone at all know about this?
Can I carry my dogs ashes onto an airplane with me?
Can I carry my dog's ashes onto an airplane with me?
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