There are a total of 10 Axioms for Field, it can be quite a challenge to remember all 10 of them offhand.
I created a mnemonic “ACIDI” to remember the 10 axioms. Unfortunately it is not a real word, but is close to the word “acidic”. A picture to remember is “acidic field”, a grass field polluted by acid rain?! 😛
Each of the properties has two parts – Addition and Multiplication. This table from Wolfram summarizes it perfectly: