Ideal quotient
id:
ideal-quotient-268-12067937
title:
Ideal quotient
text:
In abstract algebra, if I and J are ideals of a commutative ring R, their ideal quotient (I : J) is the set Then (I : J) is itself an ideal in R. The ideal quotient is viewed as a quotient because K J ⊆ I if and only if K ⊆ ( I : J ) . The ideal quotient is useful for calculating primary decompositions. It also arises in the description of the set difference in algebraic geometry (see below). (I : J) is sometimes referred to as a colon ideal because of the notation. In the context of fractional
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wiki
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encyclopedia
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original url:
https://en.wikipedia.org/wiki/Ideal_quotient
date created:
date modified:
2023-05-05T09:34:54Z
main entity:
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13
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