Should a database table that contains two columns that are foreign keys have a third column which is the primary key?

Question

I am guessing no, since the foreign keys are the primary keys in their own tables, so they will be unique.

More info

I am using MySQL and the following three tables are using the InnoDB engine.

=======================    =======================
| galleries           |    | images              |
|---------------------|    |---------------------|
| PK | gallery_id     |    | PK | image_id       |
|    | name           |    |    | title          |
|    | description    |    |    | description    |
|    | max_images     |    |    | filename       |
|    | enabled        |    |    | enabled        |
=======================    =======================

========================
| galleries_images     |
|----------------------|
| FK | gallery_id      |
| FK | image_id        |  <----- Should I add a PK to this table?
========================

---

Epilogue

Thanks for the excellent answers. I learned about composite keys and, after considering my specific case, I decided to make the image_id column in the galleries_images table a primary key. This way, images may only be associated with one gallery, which is what I want.

I am also going to implement a order_num column in galleries_images which I will use PHP logic to maintain. This way the user can put images in a specific order in each gallery. I ended up with this:

============================
| galleries_images         |
|--------------------------|
| PK, FK | image_id        |
| FK     | gallery_id      | 
|        | order_num       |
============================

Thanks again!

Epilogue II

Thanks to those of you who pointed out that I didn't even need this table. I didn't provide the most complete information to begin with. I ended up dropping the galleries_images table altogether and just added the gallery_id as a foreign key to the images table. Anyways, I still learned more than I thought I would and am grateful for the help.

Answer 1

In theory, if the combination of the two foreign keys (FKs) is unique in the table, or if the combination of the two FKs plus some other column is unique, then the table has a compound primary key and there is no strict need to introduce another key as a surrogate primary key. However, it is not unusual to find that people do add an extra key. In part, it depends on what else the data in the table with the compound primary key will used for. If it describes something that will itself have rows from other tables associated with it, then it may make sense to introduce a simple PK.

Some software seems to require simple PKs, even though the Relational Data Model does not.