The indefinite article is almost never used when the words breakfast, lunch, or dinner are written without an adjective. The above should read ‘I ate breakfast’, not ‘I ate a breakfast’. (rule 3.1)The indefinite article can be used with the words breakfast, lunch, or dinner when an adjective is used as a description.
Jim ate a big breakfast yesterday.
Sally at an amazing lunch.
Billy only has time for a quick dinner. (2nd exception to rule 3.1)