Fully wild prinjective type of posets and their quadratic forms (Q1891500)

Let \(K\) be a field and let \(KJ\) be the algebra given by the finite partially ordered set \(J\). The category \(\text{prin}(KJ)\) consisting of the prinjective \(KJ\)-modules has the following properties: it is additive, has the finite unique decomposition property, it is closed under extensions, has Auslander-Reiten sequences, and has enough relative projective and injective objects. The main purpose of this paper is to characterize the posets which are of fully wild prinjective type. Recall that a poset \(J\) is of fully wild prinjective type provided there exists a full exact functor \(T:\text{fin}(K\langle X,Y\rangle)\to\text{prin}(KJ)\) which preserves the indecomposability and respects the isomorphism classes.