On a Grätzer's problem (Q1089014)
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scientific article; zbMATH DE number 4002144
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a Grätzer's problem |
scientific article; zbMATH DE number 4002144 |
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On a Grätzer's problem (English)
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1985
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Let L be a lattice and let Sub(L) stand for the lattice of all sublattices of L. The author proves the following theorem: Let L be a modular lattice of locally finite length such that L does not admit a linear decomposition. Then Sub(L) determines L up to an isomorphism and dual isomorphism. (This is a partial answer to Problem 1.4 in the book by \textit{G. Grätzer} [General Lattice Theory (1978; Zbl 0385.06014)].)
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lattice of sublattices
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modular lattice of locally finite length
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dual isomorphism
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