Trivial Ring from Abelian Group

Theorem

An abelian group $\struct {G, +}$ may be turned into a trivial ring by defining the ring product to be:

$\forall x, y \in G: x \circ y = e_G$

Proof

Follows directly from the definition of a trivial ring.

$\blacksquare$

Sources

• 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): Chapter $1$: Rings - Definitions and Examples: $2$: Some examples of rings: Ring Example $3$