Ideal Contraction

When is a ring homomorphism and is an ideal in , then is an ideal in , called the contraction of and sometimes denoted .

The contraction of a prime ideal is always prime. For example, consider . Then the contraction of is the ideal of even integers.

See also

Algebraic Number Theory, Ideal, Ideal Extension, Prime Ideal, Ring

This entry contributed by Todd Rowland

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References

Bonsall, F. F. and Duncan, J. Complete Normed Algebras. New York: Springer-Verlag, 1973.

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Ideal Contraction

Cite this as:

Rowland, Todd. "Ideal Contraction." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/IdealContraction.html

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