𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Note on Algebras of Finite Uniserial Type

✍ Scribed by Klaus Bongartz

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
79 KB
Volume
188
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

A denotes an artin algebra in the sense of Auslander, i.e., an associative algebra of finite length over a commutative artinian ring Z. We assume in addition that Z is local and that its residue field k is algebraically closed, whence infinite. As a partial answer to a w x question raised by Auslander and propagated as an open problem in 1 we prove the next result, which gives an intrinsic inductive characterization of algebras as above having only finitely many uniserial modules up to isomorphism. Our result also confirms the second part of the conjecture w x 5.11 made by B. Zimmerman-Huisgen 3 . We refer the reader to the w x articles 2, 3 for much more information on uniserial modules and for many interesting examples.

πŸ“œ SIMILAR VOLUMES

On Cocommutative Hopf Algebras of Finite
On Cocommutative Hopf Algebras of Finite Representation Type
✍ Rolf Farnsteiner; Detlef Voigt πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 207 KB

Let G be a finite algebraic group, defined over an algebraically closed field k of characteristic p>0. Such a group decomposes into a semidirect product G=G 0 \_G red with a constant group G red and a normal infinitesimal subgroup G 0 . If the principal block B 0 (G) of the group algebra H(G) has fi

A Note on the Cohomology of Finite-Dimen
A Note on the Cohomology of Finite-Dimensional Cocommutative Hopf Algebras
✍ John H. Palmieri πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 162 KB

In the context of finite-dimensional cocommutative Hopf algebras, we prove versions of various group cohomology results: the Quillen᎐Venkov theorem on detecting nilpotence in group cohomology, Chouinard's theorem on determining whether a kG-module is projective by restricting to elementary abelian p

A Note on Diagonality of Algebras
A Note on Diagonality of Algebras
✍ Josef Ε lapal πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 171 KB πŸ‘ 1 views
A Note on Derivations of Simple Algebras
A Note on Derivations of Simple Algebras
✍ A. Elduque; F. Montaner πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 319 KB

Necessary and sufficient conditions for all the derivations of a finite dimensional simple nonassociative algebra, over a field of characteristic zero, to be inner are given in terms of the Lie multiplication algebra and the trace of the derivations. 1994 Academic Press, Inc.

A note on simple graphic algebras
A note on simple graphic algebras
✍ Juhani Nieminen πŸ“‚ Article πŸ“… 1975 πŸ› John Wiley and Sons 🌐 English βš– 223 KB πŸ‘ 1 views

A NOTE ON SIMPLE GRAPHIC ALGEBRAS by JUHANT NIEMTNEN in Helsinki (Finland) 111 troduction Several authors have studied the structure of algebras with a ternary operation called median operation, scc e.g. [I], [2], [3], [4], and [7]. Most of the authors have concentrated on the lattice and tree struc