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Every finite distributive lattice is the congruence lattice of some modular lattice

✍ Scribed by E. T. Schmidt

Book ID
112760549
Publisher
Springer
Year
1974
Tongue
English
Weight
387 KB
Volume
4
Category
Article
ISSN
0002-5240

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πŸ“œ SIMILAR VOLUMES

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✍ Yong Zhang πŸ“‚ Article πŸ“… 1996 πŸ› Springer Netherlands 🌐 English βš– 128 KB

Schmidt proved that every distributive lattice with n join-irreducible elements can be represented as the congruence lattice of a "small" lattice I,, that is, a lattice L with O(r?) elements. G. Gratzer, I. Rival, and N. Zaguia proved that, for any o < 2, O(n\*) can not be improved to O(rF). In this

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The equivalence of the following conditions on a chain \(L\) is proved: (1) \(L\) is algebraic; (2) There is a right chain domain \(T\) (with identity) such that \(L\) is isomorphic to the chain of proper two-sided ideals of \(T\) and all two-sided ideals of \(T\) are idempotent; (3) \(L\) is isomor