Sounds like one of your add-ons is alerting you to new e-mails.

What is an add-on, and what do I do about it?

P.S. I do get a copy of a new email up in the right hand corner of the screen, but what is happening that I object to is that the whole email screen keeps interrupting me. Not every time I get an email, but periodically, not on any particular schedule, and even after I've looked at the new emails. I don't have any new software; all I have done is update Foxfire when it says to, and that is when this started.

Dollhousedude said

What is an add-on, and what do I do about it?

Hello Dollhousedude,

"Add-on" is the collective name for extensions, plugins, themes and dictionaries. You'll find them in Preferences => Add-ons, or you can type in the address bar about:addons and press Enter.

As to what is happening here : I have no idea - hopefully someone else does .....

'Been searching to find a possible explanation for your email account to open while you're on another page - to no avail ....

Just a few thoughts :

Maybe an extension could be the culprit here - even though I doubt that you have any, as you didn't know what "add-ons" are.

Could it be that you inadvertently clicked on the email notification ?

Type about:support in the address bar and press Enter. Under the main banner, press the button; Copy Text To Clipboard.. Now in the Reply Box on the forum page, do a right-click in the box and select Paste.

This will show us your system details. No Personal Information Is Collected.

If you can't fit everything in one post, do not worry. It's the upper part we need to check out.