On the primary decomposition of differential ideals of strongly Laskerian rings
A commutative ring \(R\) is said to be strongly Laskerian if every ideal of \(R\) has a primary decomposition and, in addition, each primary ideal contains a power of its radical. Let \(\underline H\) be a set of higher derivations on such a ring. The author considers \(\underline H\)-differential ideals on such a ring and proves the following theorem: let \(\underline H\) be a set of higher derivations and let \(I\) be an ideal of a strongly Laskerian ring that is \(\underline H\)-differential. Then \(I\) can be represented as an irredundant intersection of a finite number of \(\underline H\)-differential primary ideals of \(R\).
scientific article; zbMATH DE number 780117