Let $R$ be a commutative ring. The characteristic of $R$ is the smallest positive integer $n$ such that $a + a + \cdots + a$ ($n$ times) is zero for every $a \in R$, if such an integer exists, and zero, otherwise. Choose the correct statement(s) from below: (A) For every $n \in \mathbb{N}$, there exists a commutative ring whose characteristic is $n$; (B) There exists an integral domain with characteristic 57; (C) The characteristic of a field is either 0 or a prime number; (D) For every prime number $p$, every commutative ring of characteristic $p$ contains $\mathbb{F}_p$ as a subring.
Let $R$ be a commutative ring. The characteristic of $R$ is the smallest positive integer $n$ such that $a + a + \cdots + a$ ($n$ times) is zero for every $a \in R$, if such an integer exists, and zero, otherwise. Choose the correct statement(s) from below:\\
(A) For every $n \in \mathbb{N}$, there exists a commutative ring whose characteristic is $n$;\\
(B) There exists an integral domain with characteristic 57;\\
(C) The characteristic of a field is either 0 or a prime number;\\
(D) For every prime number $p$, every commutative ring of characteristic $p$ contains $\mathbb{F}_p$ as a subring.