View source for Integral ideal

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An [[Ideal|ideal]] of the field $Q$ relative to a ring $A$ (here $Q$ is the field of fractions of $A$, cf. [[Fractions, ring of|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 $A$.



====Comments====
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|Fractional ideal]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  E. Weiss,   "Algebraic number theory" , McGraw-Hill  (1963)</TD></TR></table>