Category:Second Ring Isomorphism Theorem

This category contains pages concerning Second Ring Isomorphism Theorem:

Let $R$ be a ring, and let:

$S$ be a subring of $R$

$J$ be an ideal of $R$.

Then:

$(1): \quad S + J$ is a subring of $R$

$(2): \quad J$ is an ideal of $S + J$

$(3): \quad S \cap J$ is an ideal of $S$

$(4): \quad \dfrac S {S \cap J} \cong \dfrac {S + J} J$

where $\cong$ denotes group isomorphism.