Idea stealing is quite common

Are you worried about your ideas getting stolen? Idea theft is far more common than you might think.
 
Sujit from Pakistan submitted an article to a reputed journal and received a rejection letter. Later, he found another article published in a different reputed journal by Sujit from India, one of the reviewers of his paper. The theft was so poorly executed that even the manuscript document had a similar name. Caught red-handed, he came up with the lame excuse of mistakenly submitting the wrong document (link).
 
Sujit is like a petty thief who got caught in his first attempt and was soundly beaten by the crowd. But in most cases, the theft is so subtle that it becomes nearly impossible for the victim to defend their case. A friend of mine, who worked in a microbiology lab in the Netherlands, had one of his co-authored manuscripts rejected by Science, only to later see its main idea published in Nature. They did not even fight the case.

Don't assume that publishing your work protects your ideas. Almost everyone credits Einstein for the theory of relativity, even though Lorentz and Poincaré formulated key aspects of the theory before him, which is an undisputed fact. Einstein maintained that he had not read their papers, which is hard to believe given that he worked in a patent office before joining academia. Julius von Mayer nearly committed suicide and was admitted to a mental hospital because he was denied credit for his work on thermodynamics.
 
What can one do? I always recommend putting your manuscript on a preprint server if you want to protect your work from petty thieves. However, if the theft is subtle, especially when committed by a more famous scientist, there is little you can do. I am not saying you shouldn’t fight, but it is important to learn to make peace with yourself. Scientific discourse largely runs on trust, and there is no strong mechanism to prevent stealing of ideas.