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Abstract Algebra

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Maximal Cardinality of the Generating Set of a Ring

ABSALG-KTMHYI

Let $S$ be a subset of ring $R$. We say $S$ generates $R$ if every element of $R$ can be obtained from finite sums and products of elements in $S$.

If $R = \mathbb{Z}/n\mathbb{Z}$, where $n$ is even, what is the maximum cardinality of $S$?

A

$0$

B

$1$

C

$n/2 - 1$

D

$n$

E

$n^2/2$