The Class of (2, 2)-Groups With Homocyclic Regulator Quotient of Exponent  Has Bounded representation type

Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru

doi:10.1017/s1446788714000652

Cited by 2 publications

(3 citation statements)

References 8 publications

(15 reference statements)

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“…. Now det M ′ = 1, and we may assume that there is an entry 1 in position (2,2). With row transformation, we obtain…”

Section: (S Pmentioning

confidence: 99%

“…The category Rep(S, Z p m ) is related to a category of almost completely decomposable abelian groups, called (S, p m )-groups (Section 5), [2]. An (S, p m )-group is, up to near-isomorphism, uniquely the direct sum of indecomposable (S, p m )-groups, so that finding the indecomposable (S, p m )-groups amounts to a classification of these groups up to near-isomorphism.…”

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confidence: 99%

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Representations of finite posets over the ring of integers modulo a prime power

Arnold¹,

Mader²,

Mutzbauer³

et al. 2016

J. Commut. Algebra

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The classical category Rep(S, Zp) of representations of a finite poset S over the field Zp 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.

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“…. Now det M ′ = 1, and we may assume that there is an entry 1 in position (2,2). With row transformation, we obtain…”

Section: (S Pmentioning

confidence: 99%

mentioning

confidence: 99%

Representations of finite posets over the ring of integers modulo a prime power

Arnold¹,

Mader²,

Mutzbauer³

et al. 2016

J. Commut. Algebra

Self Cite

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show abstract

“…Then T cr (X) is called the critical typeset of X. The problem has been largely solved when the critical typeset is an inverted forest in a number of papers by Arnold-Mader-Mutzbauer-Solak ( [2], [3], [4], [5], [6], [7], [8], [9], [10]) using representations of posets as a tool.…”

Section: Introductionmentioning

confidence: 99%