Representations of partially ordered sets

Назарова, Л. А.; Roiter, A. V.

doi:10.1007/bf01084662

Cited by 82 publications

(80 citation statements)

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“…The other approach belongs to L.A. Nazarova and A.V. Roiter [2] who reduced these representations to solving some matrix problems over fields, i.e. the reduction of some classes of matrix by an admissible set of transformations.…”

Section: Introductionmentioning

confidence: 99%

On right hereditary SPSD-rings of bounded representation type II

Gubareni¹

2012

Sci. Res. Inst. Math. Comp. Sci.

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Section: Introductionmentioning

confidence: 99%

On right hereditary SPSD-rings of bounded representation type II

Gubareni¹

2012

Sci. Res. Inst. Math. Comp. Sci.

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“…The category @ V (as well as any subcategory in modk) can be regarded as a faithful module over itself [1]. [5] ). The criterion of finite representability of posets was obtained in [6].…”

Section: Introductionmentioning

confidence: 99%

Elementary and multielementary representations of vectroids

et al. 1995

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“…From Fig. 1 [2,6], (X 1, J1) is locally representation-finite. Observe also S~4,1 ) is a simple injective object in modF(Xl,J1) and there are no nonzero maps from S(3,a ) to indecomposable objects in modr(X 1, J1) which are not in modF(X, J).…”

Section: Proof It Is Not Hard To See That Mode(qi) Contains As a Fumentioning

confidence: 99%

Correction to Group algebras of finite representation type

Meltzer

Skowroński

1984

Math Z

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Recently we have observed that Lemma 4 in [-8] is not true and hence the characterization of group algebras of finite representation type given in [-8] is not complete.Here, we will give the correct version of [-8, Theorem] and we will complete the proof given there.We use the same notation as in E8]. In order to state the main result, we need some additional. Let F be a division algebra over a fixed field K. We will denote by Rr(1 ) the quiver algebra FQ1 (in the sense of [3]) of the quiver QI" 1~2~-3 and by RF(2 ) the opposite algebra to Rv(1 ). Moreover, we will denote by RF (3 ) the bounden quiver algebra FQz/I 2 where Q2 is the quiver ~3 ~2~ =2 3+---4and 12 is the ideal in the quiver algebra FQ2 generated by c%c%, and by Re(4 ) the opposite algebra to RF(3 ). Finally, recall that for nonnegative integers m and n, Rv(m,n ) is the bounden quiver algebra FQ,,,./Im, . where Q,,,, is the quiver quiver 9 m ;, 9 I-+ )e and Ira, . is the ideal in the quiver algebra FQm,, generated by the composed arrows fiifii+ 1, i= 1, ..., m -1, and c~j+ 1 c~j, j = 1 ..... n -1.

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Representations of partially ordered sets

Cited by 82 publications

References 1 publication

On right hereditary SPSD-rings of bounded representation type II

On right hereditary SPSD-rings of bounded representation type II

Elementary and multielementary representations of vectroids

Correction to Group algebras of finite representation type

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