Geodesic
Full and elementary nets over the quotient field of a~principal ideal ring
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 42-51

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Let $K$ be the quotient field of a principal ideal ring $R$, and $\sigma=(\sigma_{ij})$ be a full (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 diagonal matrix, all $\sigma_{ij}$ are ideals of a fixed intermediate subring $P$, $R\subseteq P\subseteq K$. 
@article{ZNSL_2017_455_a4,
     author = {R. Y. Dryaeva and V. A. Koibaev and Ya. N. Nuzhin},
     title = {Full and elementary nets over the quotient field of a~principal ideal ring},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {42--51},
     publisher = {mathdoc},
     volume = {455},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a4/}
}
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R. Y. Dryaeva; V. A. Koibaev; Ya. N. Nuzhin. Full and elementary nets over the quotient field of a~principal ideal ring. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 42-51. http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a4/