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Every countable lattice is a retract of a direct product of chains

โœ Scribed by Maurice Pouzet; Ivan Rival

Publisher
Springer
Year
1984
Tongue
English
Weight
601 KB
Volume
18
Category
Article
ISSN
0002-5240

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Every Algebraic Chain Is the Congruence
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โœ J.E. Vandenberg; J.G. Raftery ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 549 KB

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

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Consider a graded poset P with maximal and minimal elements. If every interval of rank three in P is a product of chains, and for every interval [.L ~1 of rank at least four, the open interval (x, y) is connected, we show that the entire poset is a product of chains. This proves a conjecture of Stan