Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
REPRESENTATIONS OF FINITE POSETS OVER THE RING OF INTEGERS MODULO A PRIME POWER
Date
2016-12-01
Author
Arnold, David
Mader, Adolf
Mutzbauer, Otto
Solak, Ebru
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
244
views
0
downloads
Cite This
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.
Subject Keywords
Poset
,
Representation
,
Indecomposable
,
Representation type
,
Almost completely decomposable group
URI
https://hdl.handle.net/11511/38005
Journal
JOURNAL OF COMMUTATIVE ALGEBRA
DOI
https://doi.org/10.1216/jca-2016-8-4-461
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
REPRESENTATIONS OF POSETS AND INDECOMPOSABLE TORSION-FREE ABELIAN GROUPS
Arnold, David; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (2014-03-04)
Representations of posets in certain modules are used to find indecomposable almost completely decomposable torsion-free abelian groups. For a special class of almost completely decomposable groups we determine the possible ranks of indecomposable groups and show that the possible ranks are realized by indecomposable groups in the class.
Classification of a class of torsion-free abelian groups
Solak, Ebru (2016-01-01)
The class of almost completely decomposable groups with a critical typeset of type (2, 2) and a regulator quotient of exponent <= p(2) is shown to have exactly 4 near-isomorphism classes of indecomposable groups. Every group of the class is up to near-isomorphism uniquely a direct sum of these four indecomposable groups.
Indecomposable (1,3)-Groups and a matrix problem
Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (2013-06-01)
Almost completely decomposable groups with a critical typeset of type (1, 3) and a p-primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient p (k) , either no indecomposables if k a (c) 1/2 2; only six near isomorphism types of indecomposables if k = 3; and indecomposables of arbitrary large rank if k a (c) 3/4 4.
(1,4)-GROUPS WITH HOMOCYCLIC REGULATOR QUOTIENT OF EXPONENT p(3)
Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (2015-01-01)
The class of almost completely decomposable groups with a critical typeset of type (1,4) and a homocyclic regulator quotient of exponent p(3) is shown to be of bounded representation type. There are precisely four near-isomorphism classes of indecomposables, all of rank 6.
Almost completely decomposable groups and unbounded representation type
Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (2012-01-01)
Almost completely decomposable groups with a regulating regulator and a p-primary regulator quotient are studied. It is shown that there are indecomposable such groups of arbitrarily large rank provided that the critical typeset contains some basic configuration and the exponent of the regulator quotient is sufficiently large.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
D. Arnold, A. Mader, O. Mutzbauer, and E. Solak, “REPRESENTATIONS OF FINITE POSETS OVER THE RING OF INTEGERS MODULO A PRIME POWER,”
JOURNAL OF COMMUTATIVE ALGEBRA
, pp. 461–491, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38005.