Category:Third Ring Isomorphism Theorem

This category contains pages concerning Third Ring Isomorphism Theorem:

Let $R$ be a ring.

Let:

$J, K$ be ideals of $R$

$J$ be a subset of $K$.

Then:

$(1): \quad K / J$ is an ideal of $R / J$

where $K / J$ denotes the quotient ring of $K$ by $J$

$(2): \quad \dfrac {R / J} {K / J} \cong \dfrac R K$

where $\cong$ denotes ring isomorphism.