REPRESENTATIONS OF FINITE POSETS OVER THE RING OF INTEGERS MODULO A PRIME POWER

Arnold D., Mader A., Mutzbauer O., SOLAK E.

JOURNAL OF COMMUTATIVE ALGEBRA, vol.8, no.4, pp.461-491, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.1216/jca-2016-8-4-461
  • Journal Name: JOURNAL OF COMMUTATIVE ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.461-491
  • Middle East Technical University Affiliated: Yes

Abstract

The classical category Rep(S, Z(p)) of representations of a finite poset S over the field Z(P) is extended to two categories, Rep(S,Z(p)(m)) and uRep(S, Z(p)(m)), of representations of S over the ring Z(p)(m). A list of values of S and m for which Rep(S,Z(p)(m)) or uRep(S,Z(p)(m)) has infinite representation type is given for the case that S is a forest. Applications include a computation of the representation type for certain classes of abelian groups, as the category of sincere representations in (uRep(S, Z(p)(m))) Rep(S, Z(p)(m)) has the same representation type as (homocyclic) (S, p(m))-groups, a class of almost completely decomposable groups of finite rank. On the other hand, numerous known lists of examples of indecomposable (S, p(m))-groups give rise to lists of indecomposable representations.