I know there is an option "advanced search" but I can't find an option there to exclude the links
It looks different in my screen (maybe different version) but found this in "advanced search":
action.email.include.results_link
action.email.include.view_link
Edit the alert and in the "When triggered" section, under Send Email choose the desired elements to include in email.
It looks different in my screen (maybe different version) but found this in "advanced search":
action.email.include.results_link
action.email.include.view_link