Which of the following statement(s) are true? (A) Every prime ideal of a finite commutative ring with unity is maximal. (B) A commutative ring with unity whose set of all ideals is countably infinite is necessarily a countable ring. (C) Let $R$ be a unique factorisation domain and $K$ be its field of fractions. There exists an irreducible element $\alpha \in R$ and an element $\beta \in K$ such that $\beta ^ { 2 } = \alpha$. (D) Every subring $R$ (with unity) of $\mathbb { Q }$ with $\mathbb { Z } \varsubsetneqq R \varsubsetneqq \mathbb { Q }$ has infinitely many prime ideals.
Which of the following statement(s) are true?\\
(A) Every prime ideal of a finite commutative ring with unity is maximal.\\
(B) A commutative ring with unity whose set of all ideals is countably infinite is necessarily a countable ring.\\
(C) Let $R$ be a unique factorisation domain and $K$ be its field of fractions. There exists an irreducible element $\alpha \in R$ and an element $\beta \in K$ such that $\beta ^ { 2 } = \alpha$.\\
(D) Every subring $R$ (with unity) of $\mathbb { Q }$ with $\mathbb { Z } \varsubsetneqq R \varsubsetneqq \mathbb { Q }$ has infinitely many prime ideals.