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1
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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
Content available remote

On restrictions of generic modules of tame algebras

76%
Bautista R., Pérez E., Salmerón L.
Open Mathematics
|
2013
|
tom 11
|
nr 3
423-434
EN
Given a convex algebra ∧0 in the tame finite-dimensional basic algebra ∧, over an algebraically closed field, we describe a special type of restriction of the generic ∧-modules.
3
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On the number of terms in the middle of almost split sequences over cycle-finite artin algebras

76%
Malicki P., Peña J., Skowroński A.
Open Mathematics
|
2014
|
tom 12
|
nr 1
39-45
EN
We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by 5.
4
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On Cohen-Macaulay modules over non-commutative surface singularities

76%
Drozd Y., Gavran V.
Open Mathematics
|
2014
|
tom 12
|
nr 5
675-687
EN
We generalize the results of Kahn about a correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities. As an application, we give examples of non-commutative surface singularities which are not Cohen-Macaulay finite, but are Cohen-Macaulay tame.
5
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On Hom-spaces of tame algebras

76%
Bautista R., Drozd Y., Zeng X., Zhang Y.
Open Mathematics
|
2007
|
tom 5
|
nr 2
215-263
EN
Let Λ be a finite dimensional algebra over an algebraically closed field k and Λ has tame representation type. In this paper, the structure of Hom-spaces of all pairs of indecomposable Λ-modules having dimension smaller than or equal to a fixed natural number is described, and their dimensions are calculated in terms of a finite number of finitely generated Λ-modules and generic Λ-modules. In particular, such spaces are essentially controlled by those of the corresponding generic modules.
6
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Odd H-depth and H-separable extensions

76%
Kadison L.
Open Mathematics
|
2012
|
tom 10
|
nr 3
958-968
EN
Let C n(A,B) be the relative Hochschild bar resolution groups of a subring B ⊆ A. The subring pair has right depth 2n if C n+1(A,B) is isomorphic to a direct summand of a multiple of C n(A,B) as A-B-bimodules; depth 2n + 1 if the same condition holds only as B-B-bimodules. It is then natural to ask what is defined if this same condition should hold as A-A-bimodules, the so-called H-depth 2n − 1 condition. In particular, the H-depth 1 condition coincides with A being an H-separable extension of B. In this paper the H-depth of semisimple subalgebra pairs is derived from the transpose inclusion matrix, and for QF extensions it is derived from the odd depth of the endomorphism ring extension. For general extensions characterizations of H-depth are possible using the H-equivalence generalization of Morita theory.
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