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?! ðŸ˜›
A: Associativity
C: Commutativity
I: Identity
D: Distributivity
I: Inverse
Each of the properties has two parts – Addition and Multiplication. This tableÂ from Wolfram summarizes it perfectly:
name | addition | multiplication |
associativity | ||
commutativity | ||
distributivity | ||
identity | ||
inverses |
For Group, “CAN I?” is the memorize trick:
C = Closure
A = Associalize
N = Neutral element (Identity, e)
I = Inverse
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sorry for spelling, A = Associativity
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