共查询到20条相似文献,搜索用时 15 毫秒
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Puiman Ng 《Journal of Pure and Applied Algebra》2011,215(10):2378-2384
This paper studies the existence of Auslander-Reiten sequences in subcategories of mod(Λ), where Λ is a finite dimensional algebra over a field. The two main theorems give necessary and sufficient conditions for the existence of Auslander-Reiten sequences in subcategories.
Theorem.
LetMbe a subcategory ofmod(Λ)closed under extensions and direct summands, and letMbe an indecomposable module inMsuch thatfor someinM. Then the following are equivalent.
- (i)
- has an-precover in the stable category,
- (ii)
- There is an Auslander-Reiten sequence0→X→Y→M→0inM.
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Huanhuan GuanPingzhi Yuan Xiangneng Zeng 《Journal of Combinatorial Theory, Series A》2011,118(4):1519-1524
In this note, we obtain the structure of short normal sequences over a finite abelian p-group or a finite abelian group of rank two, thus answering positively a conjecture of Gao and Zhuang for various groups. The results obtained here improve all known results on this conjecture. 相似文献
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Pingzhi Yuan 《Journal of Combinatorial Theory, Series A》2007,114(8):1545-1551
Let G be a cyclic group of order n?2 and a sequence over G. We say that S is a zero-sum sequence if and that S is a minimal zero-sum sequence if S is a zero-sum sequence and S contains no proper zero-sum sequence.The notion of the index of a minimal zero-sum sequence (see Definition 1.1) in G has been recently addressed in the mathematical literature. Let l(G) be the smallest integer t∈N such that every minimal zero-sum sequence S over G with length |S|?t satisfies index(S)=1. In this paper, we first prove that for n?8. Secondly, we obtain a new result about the multiplicity and the order of elements in long zero-sumfree sequences. 相似文献
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Stanislaw Kasjan 《Proceedings of the American Mathematical Society》2000,128(10):2885-2896
We investigate the behaviour of Auslander-Reiten sequences of modules over a finite dimensional algebra over a field under base field extension. It is proved that an Auslander-Reiten sequence splits into a direct sum of Auslander-Reiten sequences provided the extension is separable in the sense of MacLane.
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Svetoslav Savchev 《Discrete Mathematics》2007,307(22):2671-2679
A sequence in an additively written abelian group is called zero-free if each of its nonempty subsequences has sum different from the zero element of the group. The article determines the structure of the zero-free sequences with lengths greater than n/2 in the additive group Zn of integers modulo n. The main result states that for each zero-free sequence of length ?>n/2 in Zn there is an integer g coprime to n such that if denotes the least positive integer in the congruence class gai (modulo n), then . The answers to a number of frequently asked zero-sum questions for cyclic groups follow as immediate consequences. Among other applications, best possible lower bounds are established for the maximum multiplicity of a term in a zero-free sequence with length greater than n/2, as well as for the maximum multiplicity of a generator. The approach is combinatorial and does not appeal to previously known nontrivial facts. 相似文献
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A. S. Kondrat’ev I. V. Khramtsov 《Proceedings of the Steklov Institute of Mathematics》2012,277(1):43-50
A three-player game is considered in which the first and second players have dynamic superiority over the third player. Two fixed time points are specified. The game ends if either the first player captures the third player at the first time point, or the second player captures the third player at the second time point. We analyze a situation when the initial positions in the game are such that neither the first nor the second player alone can capture the third player at the specified points of time. We propose sufficient conditions on the parameters of the game under which, for given initial states of the players, the first and second players by applying some controls can guarantee that one of them will meet the third player at the prescribed moment. Simulation results for a model example are also presented. 相似文献
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Shunhua Zhang 《中国科学A辑(英文版)》1997,40(7):714-724
Let г denote a connected valued Auslander-Reiten quiver, let ℒ(γ) denote the free abelian group generated by the vertex setγ
0 and let ℒ(Γ) be the universal cover ofг with fundamental groupG. It is proved that whenγ is a finite connected valued Auslander-Reiten quiver,ℒ(γ) is a Lie subalgebra ofℋ(г), and is just the “orbit” Lie algebra ℒ(
)/G, where ℋ (г)1 is the degenerate Hall algebra ofг and ℒ(
)/G is the “orbit” Lie algebra induced by
. 相似文献
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