Ideal Contraction

The ideal contraction of an ideal under a ring homomorphism is the ideal in , sometimes denoted .

The contraction of a prime ideal is prime whenever its preimage is a proper ideal. This is automatic for ring homomorphisms preserving the multiplicative identity. For example, consider . Then the contraction of is the ideal of even integers.

See also

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

Portions of this entry contributed by Todd Rowland

Explore with Wolfram|Alpha

More things to try:

References

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

Referenced on Wolfram|Alpha

Ideal Contraction

Cite this as:

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

Subject classifications