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The Thickness of Amalgamations and Cartesian Product of Graphs

Yan Yang;  Yichao 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 Yang;  Zhong 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 Wang;  Xiao 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 .

Another version of cosupport in D ( R )

Junquan Qin;  Xiao Yan Yang — 2023

Czechoslovak Mathematical Journal

The goal of the article is to develop a theory dual to that of support in the derived category D ( R ) . This is done by introducing ‘big’ and ‘small’ cosupport for complexes that are different from the cosupport in D. J. Benson, S. B. Iyengar, H. Krause (2012). We give some properties for cosupport that are similar, or rather dual, to those of support for complexes, study some relations between ‘big’ and ‘small’ cosupport and give some comparisons of support and cosupport. Finally, we investigate the...

Left APP-property of formal power series rings

Zhongkui Liu;  Xiao 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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