Classification of -dipoles on nonorientable surfaces.
Flexibility of embeddings of bouquets of circles on the projective plane and Klein bottle.
The Thickness of Amalgamations and Cartesian Product of Graphs
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...
Semi- and nonparametric ARCH processes.
-Gorenstein projective, injective and flat modules
By analogy with the projective, injective and flat modules, in this paper we study some properties of -Gorenstein projective, injective and flat modules and discuss some connections between -Gorenstein injective and -Gorenstein flat modules. We also investigate some connections between -Gorenstein projective, injective and flat modules of change of rings.
(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras
Let be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective -modules under the condition that is a cocompatible -bimodule, we establish a recollement of the stable category . We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over .
Left APP-property of formal power series rings
A ring is called a left APP-ring if the left annihilator is right -unital as an ideal of for any element . We consider left APP-property of the skew formal power series ring where is a ring automorphism of . It is shown that if is a ring satisfying descending chain condition on right annihilators then is left APP if and only if for any sequence of elements of the ideal is right -unital. As an application we give a sufficient condition under which the ring...
-flat and -FP-injective modules
In this paper, we study the existence of the -flat preenvelope and the -FP-injective cover. We also characterize -coherent rings in terms of the -FP-injective and -flat modules.
The improvement of the value distribution on
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