An alkylammonium is any aliphatic ammonium cation.
Yes, amines can react with water to form alkylammonium salts through a process called protonation, where the amine group gains a proton from water. This results in the formation of a positively charged alkylammonium ion, which can further react with other species in solution.
Michael Anthony Desando has written: 'Dielectric and nuclear magnetic resonance studies of relaxation and micellization in alkylammonium carboxylate surfactant systems'