# Integral ideal

An ideal of the field \$Q\$ relative to a ring \$A\$ (here \$Q\$ is the field of fractions of \$A\$, cf. Fractions, ring of) that lies entirely in \$A\$. An integral ideal is an ideal in \$A\$, and, conversely, every ideal of \$A\$ is an integral ideal of the field of fractions \$Q\$ of \$A\$.