FoxDifferential.Completed.ProCIntegerCoefficients.AugmentationIdeal

4 sections | 4 files | 65 declarations

Wrapper for the FoxDifferential.Completed.ProCIntegerCoefficients.AugmentationIdeal folder.

Basic

1 files | 12 declarations | 9 Theorem | 3 Definition

The algebraic ideal generated by the standard completed augmentation generators \([h]-1\). The completed augmentation ideal itself is the kernel of the completed augmentation ma...

Closure

1 files | 3 declarations | 3 Theorem

The \(\mathbb{Z}_C\llbracket H\rrbracket\) finite-stage index is directed when both the coefficient and group-quotient classes are directed by formation closure.

FiniteStage

1 files | 20 declarations | 10 Theorem | 9 Definition | 1 Abbreviation

The augmentation ideal in one finite stage of \(\mathbb{Z}_C\llbracket H\rrbracket\).

Kernel

1 files | 30 declarations | 24 Theorem | 6 Definition

The ideal in \(R[A]\) generated by \([k]-1\) for \(k \in \ker f\).