We construct a matrix algebra Λ(A, B) from two given finite dimensional elementary algebras A and B and give some sufficient conditions on A and B under which the derived Jordan–Hölder property (DJHP) fails for Λ(A, B). This provides finite dimensional algebras of finite global dimension which do not satisfy DJHP.

中文翻译：

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不满足派生的Jordan-Hölder性质的有限维代数的示例

我们从两个给定的有限维基本代数A和B构造矩阵代数Λ（A，B），并在A和B上给出一些充分的条件，在此条件下，对于Λ（A，B）导出的Jordan-Hölder性质（DJHP）失效。这提供了不满足DJHP的有限整体维数的有限维代数。