# Integral ideal

From Encyclopedia of Mathematics

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 $A$.

#### 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.

#### References

[a1] | E. Weiss, "Algebraic number theory" , McGraw-Hill (1963) |

**How to Cite This Entry:**

Integral ideal.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Integral_ideal&oldid=33086

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article