Writing under a nom de plume

Like many writers on this site, I write under a nom de plume, and I'm wondering how this affects my rights to assert ownership over anything I write. How can I assert I am the author of a piece of work when I'm not using my own name?

I'm currently writing a piece which I may consider selling on Kindle. If I do, what's to stop other people copying the text and selling it on one of the other ebook sites, or even publishing it in hard copy?