If you want to stop receiving emails about Application Alerts, opting out of them is easy.

1.  Sign in to the network that you're receiving the Alerts from. Click on the "My Settings" link in the upper right corner of the page:

2.  Click on "Email" in the left column:

3.  Uncheck the box next to "Alerts sent via Applications":

You will no longer receive email notifications when an Application sends you an Alert.