There is one general rule we always follow when determining whether bonuses "stack" or not. You'll find it right at the beginning of the book, Chapter 1, in the Common Terms section:
Bonuses of the same "type" do not stack. Bonuses of different "types" stack. The only exception is bonuses of the type "Dodge" which do stack with eachother.
Look up Mage Armor in the rulebook. You will see that it does not give you a "+4 bonus to AC". Instead, it gives you a "+4 armor bonus to AC" so the "type" of this bonus is "armor". The Ring of Protection gives you a "deflection" bonus. Since these are different bonus types, they stack.
It's worth noting since it's a common mistake that ordinary armor like chainmail or studded leather, etc., gives you an "Armor" bonus - the same type of bonus that Mage Armor gives you. Yep, that means that Mage Armor does not stack with the armor you buy in the store. If you're wearing Leather armor (+2 armor bonus) and you cast Mage Armor on yourself (+4 armor bonus) you only get the bigger bons (+4), not both.
Final note: this general rule doesn't apply to penalties. Two penalties of the same type stack and you suffer from both. Likewise, if you have a bonus of a certain type and you also have a penalty of the same type, that stacks as well and you apply them both.
