Serial Algebras

Yurij A. Drozd and Vladimir V. Kirichenko
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Yurij A. Drozd: Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics
Vladimir V. Kirichenko: Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics

Chapter 10 in Finite Dimensional Algebras, 1994, pp 174-189 from Springer

Abstract: 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).

Keywords: Direct Summand; Division Algebra; Uniserial Algebra; Basic Algebra; Quotient Algebra (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-3-642-76244-4_10

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