Why do fix male dogs have a erections?

Its not "doing" - its humping. Humping has very little to do with dominance, and only a small chance it is a sexual-based behaviour. Most of the time, it is because the dog is anxious or over-excited, and humping is said to help relieve the building stress. It can happen both during play or after nerve-racking events.

Such behaviour can be trained out, either with "Stay/Leave It" commands, or to distract the dog with a favourite toy or playtime activity. Identifying when and where the dog begins humping is ideal, as this helps you avoid these scenariOS, or if they are unavoidable, maintain the dog's attention in another way before he becomes too stressed.

2nd ANSWER:

Humping another dog is definitely a sign of dominance. This is the most common sign.