Definition of zero in monomial ideals

Question

I am studying monomial ideals and I have a problem with this definition:

Let R=A$[X_1.....X_k]$, and: $$0=(\phi)R $$ How this ideal contains 0? Thanks

Answer 1

I think its from definition . Every ideal of a ring contains zero , then ideal generated by empty set , contains zero . Zero is an ideal of a ring contains empty set , then it contains ideal generated by empty set .