I have seen examples of other particles that decay into gluons but do gluons themselves ever decay. Since gluons are not composed of anything else I assume they are fundamental.
On there other hand some fundamental particles decay and some do not i.e the photon. But on the other other hand some non fundamental particles do not decay either. i.e proton.
Maybe I am getting tangled up in semantics. Instead of decay would transformation be a better description.
Best Answer
In the standard model of particle physics zero mass elementary particles, of which the gluon is one if you look at the table, cannot decay. This is because the standard model is formulated on fourvectors of special relativity, and has to obey basic quantum mechanical conservation laws, as energy and momentum conservation.
If a zero mass particle were to decay within this framework, the decay products (as an example two particles) would have as an invariant mass, the length of the added four vectors, . This would contradict energy and momentum conservation , as the before (gluon four vector ) and after decay(summed four vector of the two decay products) four vectors should be the same .
The gluon plays the same role as the photon for the strong interactions.