Can someone explain me the sentence about ideals?

Question

Can someone explain me the sentence:

"If $R=K[x]$ the prime ideals are $\langle f(x)\rangle $ where $f(x)$ is an irreducible polynomial in $K[x]$ and $\langle 0\rangle $, and again $\langle f(x)\rangle $ $\ f(x)$ is also maximal."

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Answer 1

The notation $\langle a_1,\dots,a_n \rangle$ for $a_i$ in a ring $R$ sometimes means the ideal generated by $a_i$. So $\langle f(x) \rangle$ is the same as $(f(x))$ in other notation, or simply the set $\{f(x)g(x): g(x) \in K[x]\}$. The statement is saying a prime ideal of $K[x]$ is either the zero ideal, or a maximal one which is of the form $\langle f(x) \rangle$ for $f(x)$ irreducible.