Representations of Finite Posets Over Discrete Valuation Rings

Abstract

Given a discrete valuation ring R, a non-negative integer m, and a finite partially ordered set S, the representation type of a category rep(S*, R, m) of finite rank free R-module representations of S is characterized in terms of S and m. As an application, representation types of some categories of torsion-free abelian groups of finite rank are determined.

Key Words:

• Finite partially ordered sets
• Modules over discrete valuation rings
• Representations

Mathematics Subject Classification:

• Primary 16G20
• Secondary 20K15

ACKNOWLEDGMENT

The research of the first author was supported by the Baylor University Research Committee. The research of the second author was supported by Polish KBN Grant PO3A 014 28.

Notes

Communicated by K. M. Rangaswamy.