What is the proper form?
send an e-mail
send a mail
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This question appears to be off-topic. The users who voted to close gave this specific reason:
First of all, it's not often that you'll find someone referring to email as "e-mail". Mostly there is no hyphen. Just a note!
To answer your question, definitely "send an email". As in:
"I'm going to send an email over to Katelyn about that."
However, while this isn't wrong, it's actually most often shortened even more, to just "email" like this:
"I'm going to email Katelyn about that."