Year: 2005
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Grätzer, George, Wehrung, Friedrich
Institution: Laboratoire de Mathématiques Nicolas Oresme
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4299801685