How do I present a current state of research and ask for ideas/guidance?

I am currently tinkering with an idea and have exhausted the possible exploration on the matter by me. I would like to present what I am doing and where I am at and hopefully ask people to show me other avenues to pursue or if they can find something interesting in it worth exploring. Maybe, they can think of how to usefully proceed in my exploration, better than I can with my "Mathematician's block".

• I am playing around with the idea of $f(x,y) f(y,z) = f(x,z)$. It's mostly playing around with abstract algebra. I am about to hit the wall on what is possible with this idea. I just want to know what other interesting things I can do with this. It's not an idea interesting enough to bother the math faculty with. It's cutting edge research or anything. – XYZT Dec 5 '14 at 7:08
• @NikhilMahajan You might want to look up "rectangular bands". If $S$ is a set, then a rectangular band is a semigroup $T:=S\times S$ with multiplication given by $(a, b)(c, d)=(a, d)$. – user1729 Dec 5 '14 at 9:33