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Cardinality of the Generating Set of an uncountable Ring

ABSALG-VTBLZQ

Let $R$ be an uncountable ring generated by a set $S$. Which of the following are possible cardinalities of $S$?

A

$1$

B

$2$

C

$|S|$ can be any (finite) prime number.

D

$S$ can be countable.

E

$S$ can be uncountable.