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2016 Representations of finite posets over the ring of integers modulo a prime power
David Arnold, Adolf Mader, Otto Mutzbauer, Ebru Solak
J. Commut. Algebra 8(4): 461-491 (2016). DOI: 10.1216/JCA-2016-8-4-461

Abstract

The classical category Rep$(S,\mathbb {Z}_{p})$ of representations of a finite poset $S$ over the field $\mathbb {Z}_{p}$ is extended to two categories, Rep$(S,\mathbb {Z}_{p^{m}})$ and uRep$(S,\mathbb {Z}_{p^{m}})$, of representations of $S$ over the ring $\mathbb {Z}_{p^{m}}$. A list of values of $S$ and $m$ for which Rep$(S,\mathbb {Z}_{p^{m}})$ or uRep$(S,\mathbb {Z}_{p^{m}})$ 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$(S,\mathbb {Z}_{p^{m}})$) 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.

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David Arnold. Adolf Mader. Otto Mutzbauer. Ebru Solak. "Representations of finite posets over the ring of integers modulo a prime power." J. Commut. Algebra 8 (4) 461 - 491, 2016. https://doi.org/10.1216/JCA-2016-8-4-461

Information

Published: 2016
First available in Project Euclid: 27 October 2016

zbMATH: 1373.16032
MathSciNet: MR3566526
Digital Object Identifier: 10.1216/JCA-2016-8-4-461

Subjects:
Primary: 16G20, 16G60, 20K15
Secondary: 20K25

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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Vol.8 • No. 4 • 2016
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