You'll find some of the solutions that work best for me here soon. And let me know about your solutions and opinions.
Turn your email notification off!
Yes, correctly. Ignore these mails for a given amount of time. All the notifications only distract you from dealing with your current task. Let the emails be were they are. No one sends you an email if its reeeeally urgent (=life threatening) or needs an immediate reply within the next few minutes.
Try out what works best for you. Some check their inbox once or twice a day (morning or evening), others once every hour and others after they have finished a (self-assigned) task.
You're in charge of the inbox, not the other way round.