Answer by rschwieb for Every commutative ring of characteristic $p$ contains...
Another example would be the ideal $A=(X)$ in $F_p[X]$. It's a rng of characteristic $p$, but it can't contain $F_p$ since the only idempotent element is $0$.
View ArticleAnswer by Pierre-Guy Plamondon for Every commutative ring of characteristic...
Not necessarily. Consider, in $\mathbb{Z}/4\mathbb{Z}$, the subring $R=\{\bar 0, \bar 2\}$. Then it has characteristic $2$, but as a ring, it does not contain $\mathbb{F}_2$, since it has only two...
View ArticleEvery commutative ring of characteristic $p$ contains $\mathbb F_p$ as a...
I know that if a commutative ring with unity is of characteristic $p$ then it will contain $\mathbb F_p$ as a subring, but if the ring is commutative with characteristic $p$ and without unity then is...
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