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Ideal Quotient

The ideal quotient (a:b) is an analog of division for ideals in a commutative ring R,

(a:b)={x in R:xb subset a}.

The ideal quotient is always another ideal.

However, this operation is not exactly like division. For example, when R is the ring of integers, then (<12>:<2>)=<6>, which is nice, while (<12>:<5>)=<12>), which is not as nice.

See also

Algebraic Geometry, Algebraic Number Theory, Ideal

This entry contributed by Todd Rowland

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Cite this as:

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

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