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Modules with semiregular endomorphism rings

100%
Yamagata K.
Colloquium Mathematicum
|
2008
|
tom 113
|
nr 2
241-250
EN
We characterize the semiregularity of the endomorphism ring of a module with respect to the ideal of endomorphisms with large kernel, and show some new classes of modules with semiregular endomorphism rings.
2
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A general form of non-Frobenius self-injective algebras

64%
Skowroński A., Yamagata K.
Colloquium Mathematicum
|
2006
|
tom 105
|
nr 1
135-141
EN
Applying the classical work of Nakayama [Ann. of Math. 40 (1939)], we exhibit a general form of non-Frobenius self-injective finite-dimensional algebras over a field.
3
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On selfinjective algebras of tilted type

64%
Skowroński A., Yamagata K.
Colloquium Mathematicum
|
2015
|
tom 141
|
nr 1
89-117
EN
We provide a characterization of all finite-dimensional selfinjective algebras over a field K which are socle equivalent to a prominent class of selfinjective algebras of tilted type.
4
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On selfinjective artin algebras having nonperiodic generalized standard Auslander-Reiten components

64%
Skowroński A., Yamagata K.
Colloquium Mathematicum
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2003
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tom 96
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nr 2
235-244
EN
We describe the structure of all selfinjective artin algebras having at least three nonperiodic generalized standard Auslander-Reiten components. In particular, all selfinjective artin algebras having a generalized standard Auslander-Reiten component of Euclidean type are described.
5
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Symmetric Hochschild extension algebras

51%
Ohnuki Y., Takeda K., Yamagata K.
Colloquium Mathematicum
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1999
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tom 80
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nr 2
155-174
EN
By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule $Hom_K(A,K)$. We study the problem of when extension algebras of a K-algebra A are symmetric. (1) For an algebra A= KQ/I with an arbitrary finite quiver Q, we show a sufficient condition in terms of a 2-cocycle for an extension algebra to be symmetric. (2) Let L be a finite extension field of K. By using a given 2-cocycle of the K-algebra L, we construct a 2-cocycle of the K-algebra LQ for an arbitrary finite quiver Q without oriented cycles. Then we show a criterion on L for all those K-algebras LQ to have symmetric non-splittable extension algebras defined by the 2-cocycles.
6
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Finiteness of the strong global dimension of radical square zero algebras

51%
Kerner O., Skowroński A., Yamagata K., Zacharia D.
Open Mathematics
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2004
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tom 2
|
nr 1
103-111
EN
The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density of the push-down functors associated to the canonical Galois coverings of the trivial extensions of algebras by their repetitive algebras.
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