Most journals formalize this process by assigning one or more referees to submitted papers. The referee is an expert in the area and can see if the result is new, correct and significant enough to be worth publishing. If you are not sure, return to step one and spend more time in the library reading, or online asking where you might read. Journals do mathematicians a favor by being the vehicles for our dialog. If you have shared your results as suggested above, then your intellectual ownership is well established.
Most mathematicians are honest, hard working, and have no desire to take another's work.