Examples of Finite Dimensional Algebras which do not Satisfy the Derived Jordan–Hölder Property

Abstract

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. MSC 2010 classification: 16E35, 18E30, 16G20