Ideal quotient

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 $IJ \subset K$ if and only if $I \subset K : J$ . The ideal quotient is useful for calculating primary decompositions. It also arises in the description of the set difference in algebraic geometry (see below).

单词	Ideal quotient
释义	Ideal quotient 英语百科 Ideal quotient 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 $IJ \subset K$ if and only if $I \subset K : J$ . The ideal quotient is useful for calculating primary decompositions. It also arises in the description of the set difference in algebraic geometry (see below).
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