Exercise 2.2.8 (Trivial Ring)

Question

The trivial ring or zero ring is the one-element set
with its only possible ring structure. Show that the only ring in which
$0 = 1$ is the trivial ring.

Hassaan Naeem · Accepted Answer

\paragraph{Solution:} Let $(R, +, \cdot)$ be our commutative, unital ring.\
If $1=0$ in $R$, then $\forall r \in R$ we have $r= 1r = 0r = 0\quad \square$

Exercise 2.2.8 (Trivial Ring)

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Exercise 2.2.8 (Trivial Ring)

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