Abstract
We prove the following theorem. Let (a 1, . . . , a m , c 12, . . . , c 1m ) be a spanning von Neumann m-frame of a modular lattice L, and let (u 1, . . . , u n , v 12, . . . , v 1n ) be a spanning von Neumann n-frame of the interval [0, a 1]. Assume that either m ≥ 4, or L is Arguesian and m ≥ 3. Let R* denote the coordinate ring of (a 1, . . . , a m , c 12, . . . , c 1m ). If n ≥ 2, then there is a ring S* such that R* is isomorphic to the ring of all n × n matrices over S*. If n ≥ 4 or L is Arguesian and n ≥ 3, then we can choose S* as the coordinate ring of (u 1, . . . , u n , v 12, . . . , v 1n ).
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Presented by F. Wehrung.
Dedicated to László Szabó on his sixtieth birthday
This research was partially supported by the NFSR of Hungary (OTKA), grant nos. K 77432 and K 60148.
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Czédli, G., Skublics, B. The ring of an outer von Neumann frame in modular lattices. Algebra Univers. 64, 187–202 (2010). https://doi.org/10.1007/s00012-010-0098-8
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DOI: https://doi.org/10.1007/s00012-010-0098-8