Barry, I personally find the default mail client horrible for the android platform. I don't understand why they've not work on creating a nice app.... actually maybe the want everybody to user gmail, but that app is bad too.
I've installed K-9 and that app is a very nice mail client. It has the ability to turn off notification as one of the many configurable items. You might want to look into this app if you wish to read email from a different email account.
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