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Serial Algebras

In: Finite Dimensional Algebras

Author

Listed:
  • Yurij A. Drozd

    (Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics)

  • Vladimir V. Kirichenko

    (Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics)

Abstract

Corollaries 9.4.2 and 9.4.3 provide a simple description of modules over uniserial algebras. However, it is easy to see that this description uses not so much the fact that all quotient algebras are quasi-Frobenius as that they all possess bijective modules. In this chapter we shall consider a more general class, the class of serial algebras, also introduced by T. Nakayama, which are characterized by the fact that each of their quotient algebras has a bijective module. We shall show that this is the most general class of algebras for which statements similar to those of Corollaries 9.4.2 and 9.4.3 hold. The structure of serial algebras is substantially more involved than that of uniserial algebras. However, under rather general assumptions, we can obtain a complete description of these algebras (the main results have been obtained by H. Kupisch).

Suggested Citation

  • Yurij A. Drozd & Vladimir V. Kirichenko, 1994. "Serial Algebras," Springer Books, in: Finite Dimensional Algebras, chapter 10, pages 174-189, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-76244-4_10
    DOI: 10.1007/978-3-642-76244-4_10
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