Mathematische Annalen

, Volume 315, Issue 3, pp 341–362 | Cite as

Unique tensor factorization of algebras

  • Michael Nüsken
Original article


Tensor product decomposition of algebras is known to be non-unique in many cases. But, as will be shown here, a \(\oplus\)-indecomposable, finite-dimensional \(\mathbb{C}\)-algebra A has an essentially unique tensor factorization \(\) into non-trivial, \(\otimes\)-indecomposable factors \(A_{i}\). Thus the semiring of isomorphism classes of finite-dimensional \(\mathbb{C}\)-algebras is a polynomial semiring \(\mathbb{N}[\mathcal{X}]\). Moreover, the field \(\mathbb{C}\) of complex numbers can be replaced by an arbitrary field of characteristic zero if one restricts oneself to schurian algebras.

Mathematics Subject Classification (1991):16 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Michael Nüsken
    • 1
  1. 1.Universität Paderborn, FB 17, D-33095 Paderborn, Germany (;˜nuesken/) DE

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