Full and Elementary Nets over the Quotient Field of a Principal Ideal Ring

Аннотация

Let K be the quotient field of a principal ideal ring R, and let σ = (σ_ij) be a full (respectively, elementary) net of order n ≥ 2 (respectively, n ≥ 3) over K such that the additive subgroups σ_ij are nonzero R-modules. It is proved that, up to conjugation by a diagonal matrix, all σ_ij are ideals of a fixed intermediate subring P, R ⊆ P ⊆ K.