Flat semilattices

Details Flat semilattices Flat semilattices

2005-01-25

arxiv.org/abs/math/0501431v1

Colloquium Mathematicum 79, no. 2 (1999) 185--191

Mathematics

General Mathematics

Scientific paper

Let $A$, $B$, and $S$ be (v,0)-semilattices and let $f: A\to B$ be a (v,0)-embedding. Then the canonical map, $f \otimes \id\_S$, of the tensor product $A \otimes S$ into the tensor product $B \otimes S$ is not necessarily an embedding. The (v,0)-semilattice $S$ is flat, if for every embedding $f : A\to B$, the canonical map $f\otimes\id$ is an embedding. We prove that a (v,0)-semilattice $S$ is flat if and only if it is distributive.

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