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The Thickness of Amalgamations and Cartesian Product of Graphs

Yan YangYichao Chen — 2017

Discussiones Mathematicae Graph Theory

The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study the thickness...

C -Gorenstein projective, injective and flat modules

Xiao Yan YangZhong Kui Liu — 2010

Czechoslovak Mathematical Journal

By analogy with the projective, injective and flat modules, in this paper we study some properties of C -Gorenstein projective, injective and flat modules and discuss some connections between C -Gorenstein injective and C -Gorenstein flat modules. We also investigate some connections between C -Gorenstein projective, injective and flat modules of change of rings.

(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras

Chao WangXiao Yan Yang — 2017

Czechoslovak Mathematical Journal

Let Λ = A M 0 B be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective Λ -modules under the condition that M is a cocompatible ( A , B ) -bimodule, we establish a recollement of the stable category Ginj ( Λ ) ¯ . We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over Λ .

Left APP-property of formal power series rings

Zhongkui LiuXiao Yan Yang — 2008

Archivum Mathematicum

A ring R is called a left APP-ring if the left annihilator l R ( R a ) is right s -unital as an ideal of R for any element a R . We consider left APP-property of the skew formal power series ring R [ [ x ; α ] ] where α is a ring automorphism of R . It is shown that if R is a ring satisfying descending chain condition on right annihilators then R [ [ x ; α ] ] is left APP if and only if for any sequence ( b 0 , b 1 , ) of elements of R the ideal l R ( j = 0 k = 0 R α k ( b j ) ) is right s -unital. As an application we give a sufficient condition under which the ring...

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