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Ideal Contraction


When f:A->B is a ring homomorphism and b is an ideal in B, then f^(-1)(b) is an ideal in A, called the contraction of b and sometimes denoted b^c.

The contraction of a prime ideal is always prime. For example, consider f:Z->Z[sqrt(2)]. Then the contraction of <sqrt(2)> 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.

Referenced on Wolfram|Alpha

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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