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Locally adequate semigroup algebras

100%
Ji Y., Luo Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
29-48
EN
We build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaĭne idempotents. This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant [...] 0-J*$0{\rm{ - }}{\cal J}*$-simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the [...] ℛ*${\cal R}*$-classes of the semigroup obtained from the above multiplicative basis. Finally, for some special cases, we provide a description of the projective indecomposable modules and determine the representation type.
2
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On homological classification of pomonoids by GP-po-flatness ofS-posets

81%
Liang X., Feng X., Luo Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
767-782
EN
In this paper, we introduce GP-po-flatness property of S-posets over a pomonoid S, which lies strictly between principal weak po-flatness and po-torsion freeness. Furthermore, we investigate the homological classification problems of pomonoids by using this new property. Finally, we consider direct products of GP-po-flat S-posets. As an application, characterizations of pomonoids over which direct products of nonempty families of principally weakly po-flat S-posets are principally weakly po-flat are obtained, and some results of Khosravi, R. in a certain extent are generalized.
3
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Tricyclic graphs with exactly two main eigenvalues

81%
Fan X., Luo Y., Gao X.
Open Mathematics
|
2013
|
tom 11
|
nr 10
1800-1816
EN
An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. Let G 0 be the graph obtained from G by deleting all pendant vertices and δ(G) the minimum degree of vertices of G. In this paper, all connected tricyclic graphs G with δ(G 0) ≥ 2 and exactly two main eigenvalues are determined.
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