ACTA issues

The extension monoid product of preinjective and preprojective Kronecker modules

István Szöll?si

Acta Sci. Math. (Szeged) 80:3-4(2014), 419-432

Abstract. Let $P,P^\prime $ be preprojective and $I,I^\prime $ preinjective Kronecker modules. Working with the extension monoid product, we give conditions for the existence of short exact sequences of the form $0\to P\to I\to I^\prime \to0$ (and dually for $0\to P^\prime \to P\to I\to0$). We show that the existence of these short exact sequences is equivalent with the existence of certain short exact sequences of preinjective (respectively preprojective) Kronecker modules, hence they obey the combinatorial rule described in [SzSz2].

DOI: 10.14232/actasm-012-315-9

AMS Subject Classification (1991): 16G20

Keyword(s): Kronecker algebra, Kronecker module, extension monoid product

Received August 30, 2012, and in revised form April 23, 2013. (Registered under 65/2012.)