More like 2 hours on a good day. Longer with traffic. Certainly not commuting distance.
Ajman is not next to Dubai either. Sharjah is in between.
There is very little to do in Ajman and few people go there. There are reasons as to why it is so cheap...
I note the poster actually said he was planning in buying in Dubai,. I trust he has now looked at a map and understands the difference?
_