This is somewhat tricky articles case:

For a background on X, see ..


For background on X, see ..

By background, I mean background about a specific topic to build knowledge on it.

  • Both are possible. You would use the indefinite article if you are talking about one of many countable backgrounds, but omit the article if you are talking about background in a generic, mass noun sense. (You can also use the definite article if it's a countable and you're specifying a specifically identified background among many.) – Jason Bassford Feb 26 at 21:37

It sounds more complete to say:

For a background on X, see ...

The form without the indefinite article somehow sounds incomplete.

If you use the indefinite article, it is not self-understood that the background is just a slice of information. It can be many slices of information from many areas, but all these slices together do not provide 100% of the background.

If you use the definite article:

For the background on X, see ...

than the referenced "location" ("see ...") is supposed to provide all the details.

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