Ideal is Subring

Theorem

Let $\struct {R, +, \circ}$ be a ring, and let $J$ be an ideal of $R$.


Then $J$ is a subring of $R$.


Proof

This follows directly from the definition of an ideal and Subring Test.

$\blacksquare$


Sources

  • 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $22$. New Rings from Old
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