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Modules with semiregular endomorphism rings

Kunio Yamagata — 2008

Colloquium Mathematicae

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.

Symmetric Hochschild extension algebras

Yosuke OhnukiKaoru TakedaKunio Yamagata — 1999

Colloquium Mathematicae

By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule H o m 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...

Finiteness of the strong global dimension of radical square zero algebras

Otto KernerAndrzej SkowrońskiKunio YamagataDan Zacharia — 2004

Open Mathematics

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...

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