Flat semilattices

Grätzer, George ; Wehrung, Friedrich

HAL, hal-00004047 / Harvested from HAL

Résumé

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.

Détail

Publié le : 1999-07-05
Classification:  Tensor product,  semilattice,  lattice,  antitone,  flat,  06B05, 06B10, 06A12, 08B25,  [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]