NH3+H2O = ? decomposition right?

NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq)

This is called dissociation, ionization or hydrolysis.

Decomposition is the change of a substance into two or more simpler substances. This is NOT a decomposition reaction.

The NH3 dissolves in the water to produce a solution of NH3
A small quantity reacts with the water:
NH3(g) + H2O(l) → NH4+(aq) + OH- (aq)
Because of the presence of the OH- group , the solution is basic.
There is no compound NH4OH produced.
This is not a decomposition reaction. The better description is a dissociation reaction.