## Tameness criterion for posets with zero-relations and three-partite subamalgams of tiled orders

### Volume 91 / 2002

Colloquium Mathematicum 91 (2002), 39-68
MSC: 16G20, 16G30, 16G50, 16G60.
DOI: 10.4064/cm91-1-4

#### Abstract

A criterion for tame prinjective type for a class of posets with zero-relations is given in terms of the associated prinjective Tits quadratic form and a list of hypercritical posets. A consequence of this result is that if ${\mit\Lambda }^{\bullet }$ is a three-partite subamalgam of a tiled order then it is of tame lattice type if and only if the reduced Tits quadratic form ${\bf q}_{{\mit\Lambda }^{\bullet }}$ associated with ${\mit\Lambda }^{\bullet }$ in [26] is weakly non-negative. The result generalizes a criterion for tameness of such orders given by Simson [28] and gives an affirmative answer to [28, Question 4.7].