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Integral ideal

From Encyclopedia of Mathematics
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An ideal of the field relative to a ring (here is the field of fractions of , cf. Fractions, ring of) that lies entirely in . An integral ideal is an ideal in , and, conversely, every ideal of is an integral ideal of the field of fractions of .


Comments

An ideal of the field relative to a ring is an -submodule of the -module . 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