Intermediate Ideals

IntermediateIdeals(I, J) : AlgEtQIdl, AlgEtQIdl -> SetIndx[AlgEtQIdl]

    Minimal: BoolElt                    Default: false

    Maximal: BoolElt                    Default: false

    PrescribedMultiplicatorRing: BoolElt Default: false

Given fractional S-ideals J ⊂I, returns all the fractional S-ideals K such that J ⊂K ⊂I.

If Minimal is set true, only the minimal ideals are returned. If Maximal is set true, only the maximal ideals are returned. If PrescribedMultiplicatorRing is set true, only ideals K with (K:K) = S are returned. The computation is done recursively starting with the minimal or maximal ones.

IntermediateIdeals(I, J, O) :AlgEtQIdl, AlgEtQIdl, AlgEtQOrd -> SetIndx[AlgEtQIdl]

    PrescribedMultiplicatorRing: BoolElt Default: false

Given fractional S-ideals I and J and an order O such that S ⊆O, J ⊆I, and O ⊆(I:I), this function returns all the fractional S-ideals K such that

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J ⊆K ⊆I, and

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O .K = I.

If PrescribedMultiplicatorRing is set true, then the output contains only K such that (K:K)=S. Note that the output may contain I. The output is produced by recursively computing maximal intermediate ideals.

IntermediateIdeals(I, J, N) : AlgEtQIdl, AlgEtQIdl, RngIntElt->SetIndx[AlgEtQIdl]

Given ideals J ⊂I over the same order, and a positive integer N, it returns all the ideals K such that

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J ⊂K ⊂I, and

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[I:K]=N.

These are computed by recursively searching for maximal submodules.