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A new local criterion for the lattice property (1994)

Ziegler, Günter M.

Springer

Algebra universalis 31 (1994), S. 608-610

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ISSN: 1420-8911

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We prove that a bounded poset of finite length is a lattice if and only if the following condition holds: whenever two elementsx 1,x 2 that cover a common elementx are both smaller that two elementsy 1,y 2 that are covered by a common elementy, then there exists an elementz that is an upper bound forx 1,x 2 and a lower bound fory 1,y 2.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01236510

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