FULL AND ELEMENTARY NETS OVER THE QUOTIENT FIELD OF A PRINCIPAL IDEAL RING

摘要

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 .