Why the arrhenius model of acids and base does not include ammonia in a solution as a base?

According to Arrhenius model acid and base are defined as,

             Acid:
                    A substance which when dissolved in water produces H⁺ Ions is called as Arrhenius Acid.

Example:
                                 HCl        →       H⁺ ₍aq₎ +  Cl⁻ ₍aq₎

                                 HNO₃     →       H⁺ ₍aq₎  +  NO₃⁻ ₍aq₎

                                 H₂SO₄    →       2 H⁺ ₍aq₎  +  SO₄⁻² ₍aq₎

             Base:
                    A substance which when dissolved in water produces OH⁻ Ions is called as Arrhenius Acid.

Example:
                                 NaOH        →       Na⁺ ₍aq₎ +  OH⁻ ₍aq₎

                                 Mg(OH)₂    →       Mg²⁺ ₍aq₎  +  2 OH⁻ ₍aq₎

                                 Sr(OH)₂     →       Sr²⁺ ₍aq₎  +  2 (OH)₂ ₍aq₎

Ammonia (NH₃) is not arrhenius base because it does dot produce OH⁻ ions in water. Therefore, the basicity of ammonia is explained by Bronsted Lowery concept of acids and bases. And according to Bronsted Lowery concept ammonia is abase because it tends to accept  H⁺ as follow,

                                 NH₃  +  H⁺    →    NH₄⁺