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A converse to the Sholander embedding

✍ Scribed by M.F. Janowitz

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
274 KB
Volume
87
Category
Article
ISSN
0012-365X

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✦ Synopsis

Janowitz, M.F., A converse to the Sholander embedding, Discrete Mathematis 87 (1991) 315-318.

It is both a well-known and useful fact that every median semilattice M may be embedded into a distributive lattice D so that M is an order ideal of D, and every element of M is the join of finitely many elements of D. However, the converse of this assertion is false. The present paper establishes several sets of necessary and sufficient conditions for an order ideal of a distributive lattice to be a median semilattice.

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