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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. 相似文献
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A. Boussaïri 《Discrete Mathematics》2009,309(10):3404-3407
Given a digraph G=(V,A), the subdigraph of G induced by a subset X of V is denoted by G[X]. With each digraph G=(V,A) is associated its dual G?=(V,A?) defined as follows: for any x,y∈V, (x,y)∈A? if (y,x)∈A. Two digraphs G and H are hemimorphic if G is isomorphic to H or to H?. Given k>0, the digraphs G=(V,A) and H=(V,B) are k-hemimorphic if for every X⊆V, with |X|≤k, G[X] and H[X] are hemimorphic. A class C of digraphs is k-recognizable if every digraph k-hemimorphic to a digraph of C belongs to C. In another vein, given a digraph G=(V,A), a subset X of V is an interval of G provided that for a,b∈X and x∈V−X, (a,x)∈A if and only if (b,x)∈A, and similarly for (x,a) and (x,b). For example, 0?, {x}, where x∈V, and V are intervals called trivial. A digraph is indecomposable if all its intervals are trivial. We characterize the indecomposable digraphs which are 3-hemimorphic to a non-indecomposable digraph. It follows that the class of indecomposable digraphs is 4-recognizable. 相似文献
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Zhu Fuzu 《数学年刊B辑(英文版)》1994,15(3):349-360
CONSTRUCTIONOFINDECOMPOSABLEDEFINITEHERMITIANFORMS¥ZHUFUZU(DepartmelltofMathematics,EastChinaNormalUniversitytShanghai200062,... 相似文献
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Xiaojiang Tan 《数学学报(英文版)》1995,11(3):232-246
LetX be a generic smooth irreducible complex projective curve of genusg withg4. In this paper, we generalize the existence theorem of special divisors to high dimensional indecomposable vector bundles. We give a necessary and sufficient condition on the existence ofn-dimensional indecomposable vector bundlesE onX with det(E)=d, dimH
0(X,E)h. We also determine under what condition the set of all such vector bundles will be finite and how many elements it contains.Project partly supported by the National Natural Science Foundation of China. 相似文献
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Fuzu Zhu 《数学学报(英文版)》1995,11(3):291-299
In this paper, for any given natural numbersn anda, we can construct explicitly positive definite indecomposable integral Hermitian forms of rankn over
with discriminanta, with the following ten exceptions:n=2,a=1, 2, 4, 10;n=3,a=1, 2, 5;n=4,a=1;n=5,a=1; andn=7,a=1. In the exceptional cases there are no forms with the desired properties. The method given here can be applied to solving the problem of constructing indecomposable positive definite HermitianR
m
-lattices of any given rankn and discriminanta, whereR
m
is the ring of algebraic integers in an imaginary quadratic field
with class number unity. 相似文献
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In this paper,the authors construct a φ-group for n submodules,which generalizes the classical K-theory and gives more information than the classical ones.This theory is related to the classification theory for indecomposable systems of n subspaces. 相似文献
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Y. Boudabbous 《Discrete Mathematics》2009,309(9):2839-2846
Given a directed graph G=(V,A), the induced subgraph of G by a subset X of V is denoted by G[X]. A subset X of V is an interval of G provided that for a,b∈X and x∈V?X, (a,x)∈A if and only if (b,x)∈A, and similarly for (x,a) and (x,b). For instance, 0?, V and {x}, x∈V, are intervals of G, called trivial intervals. A directed graph is indecomposable if all its intervals are trivial, otherwise it is decomposable. Given an indecomposable directed graph G=(V,A), a vertex x of G is critical if G[V?{x}] is decomposable. An indecomposable directed graph is critical when all its vertices are critical. With each indecomposable directed graph G=(V,A) is associated its indecomposability directed graph defined on V by: given x≠y∈V, (x,y) is an arc of if G[V?{x,y}] is indecomposable. All the results follow from the study of the connected components of the indecomposability directed graph. First, we prove: if G is an indecomposable directed graph, which admits at least two non critical vertices, then there is x∈V such that G[V?{x}] is indecomposable and non critical. Second, we characterize the indecomposable directed graphs G which have a unique non critical vertex x and such that G[V?{x}] is critical. Third, we propose a new approach to characterize the critical directed graphs. 相似文献