Full and elementary nets over the quotient field of a principal ideal ring. (English. Russian original) Zbl 1401.16031

J. Math. Sci., New York 234, No. 2, 141-147 (2018); translation from Zap. Nauchn. Semin. POMI 455, 42-51 (2017).
Summary: Let \(K\) be the quotient field of a principal ideal ring \(R\), and let \(\sigma = (\sigma_{ij})\) be a full (respectively, elementary) net of order \(n\geq2\) (respectively, \(n\geq3\)) over \(K\) such that the additive subgroups \(\sigma_{ij}\) are nonzero \(R\)-modules. It is proved that, up to conjugation by a diagonal matrix, all \(\sigma_{ij}\) are ideals of a fixed intermediate subring \(P\), \(R\subseteq P\subseteq K\).


16S50 Endomorphism rings; matrix rings
16S34 Group rings
20H05 Unimodular groups, congruence subgroups (group-theoretic aspects)
13F10 Principal ideal rings
Full Text: DOI MNR


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