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
-
J ⊆K ⊆I, and
-
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
-
J ⊂K ⊂I, and
-
[I:K]=N.

These are computed by recursively searching for maximal submodules.

V2.29, 21 October 2025