Die Struktur n-reihiger Algebren. (English) Zbl 0537.16017
A finite dimensional algebra A over an algebraically closed field is called n-serial, if the radical of every indecomposable projective left or right A-module is the sum of at most n uniserial submodules and if moreover the intersection of any two of these submodules is zero or simple. The authors show that an n-serial algebra A for which the cycle- condition of J. P. Jans holds, has a multiplicative Cartan-basis. In this case A is isomorphic to its standard algebra and its Stammalgebra.
Reviewer: W.Müller
MSC:
| 16P10 | Finite rings and finite-dimensional associative algebras |
| 16Gxx | Representation theory of associative rings and algebras |
| 16D70 | Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) |
Keywords:
finite dimensional algebra; radical; uniserial submodules; n-serial algebra; cycle-condition; Cartan-basis; standard algebra; StammalgebraReferences:
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