Nilpotent crossed modules of commutative algebras (Q2895176)

A crossed module of commutative algebras is an algebra morphism \(\mu\) such that the target algebra acts on the source algebra. In addition, one requires that: 1) \(\mu\) be compatible with the actions of the target on itself and and the source, and 2) the action of the source on itself coincide with its own twist by \(\mu\). The author introduces and studies properties of a product of crossed ideals of crossed modules. In particular, the notion of a nilpotent crossed module is considered.NEWLINENEWLINEUnfortunately, the reading of the paper presents substantial challenges. The language is minimalistic in some parts and simply inadequate in others. This is compounded by puzzling misprints, and rather fuzzy assumptions. For example, at the beginning of Section 2, the author makes what appears to be a blanket assumption that \(R\) is an algebra with identity. Yet, two pages later an assumption is made that the annihilator of \(R\) is zero or that \(R^{2} = R\), both of which are automatic for unital algebras. Another hurdle for the reviewer - and presumably for the reader - is a surprisingly unprofessional typography.NEWLINENEWLINEOn the positive side, the paper contains some illuminating examples.