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 $A$.
An ideal of the field $Q$ relative to a ring $A\subset Q$ is an $A$-submodule of the $A$-module $Q$. These are also called fractional ideals, cf. Fractional ideal.
|[a1]||E. Weiss, "Algebraic number theory" , McGraw-Hill (1963)|
Integral ideal. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Integral_ideal&oldid=33086