Isomorphism invariants for linear quasigroups (Q2180105)

For a unital ring \(S\), an \(S\)-linear quasigroup is a unital \(S\)-module with automorphisms \(\rho\) and \(\lambda\) giving a (nonassociative) multiplication \(x\cdot y=x^{\rho}+y^{\lambda}\). The paper investigates the isomorphism problem for \(\mathbb{Z}\)-linear quasigroups. For a subclass of \(\mathbb{Z}\)-linear quasigroups, equivalences of the corresponding ordinary representations are realized by permutational intertwinings.