Discussiones Mathematicae General Algebra and Applications 22(2) (2002) 153-159
doi: 10.7151/dmgaa.1054

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FROBENIUS n-GROUP ALGEBRAS

Biljana Zeković

Faculty of Science, University of Montenegro
P.O. Box 211
8-1000 Podgorica
Serbia and Montenegro
e-mail:
biljanaz@cg.yu

Abstract

Frobenius algebras play an important role in the representation theory of finite groups. In the present work, we investigate the (quasi) Frobenius property of n-group algebras. Using the (quasi-) Frobenius property of ring, we can obtain some information about constructions of module category over this ring ([2], p. 66-67).

Keywords: n-ary group (n-group, polyadic group), (2,n)-ring, n-group-ring (algebra), (quasi-) Frobenius property, Artinianity property, regular bilinear from, descending chain condition for left (right) ideals, univeral enveloping (or covering) group, annhilator.

2000 Mathematics Subject Classification: 20N15, 20C05, 20C07, 16S34, 17A40.

References

[1]
V.A. Artamonov, Free n-groups (Russian), Mat. Zametki 8 (1970), 499-507.
[2]
L.A. Bokut, I.V. L'vov and V.K. Kharchenko, Nonkommutative Rings (Russian), vol. 18 of ``Itogi Nauki i Tekhniki", Izdat. VINITI, Moscov 1988.
[3]
A.G. Kurosh, General Algebra. - Lectures of the 1969-1970 Academic Year (Russian), Izdat, ``Nauka", Moscov 1974.
[4]
E.L. Post, Polyadic groups, Trans. Amer. Math. Soc. 48 (1940), 208-350.
[5]
B. Zeković and V.A. Artamonov, n-Group rings and their radicals (Russian), Abelian Groups and Modules (Tomsk), 11 (1992), 3-7 (in Russian).
[6]
B. Zeković and V.A. Artamonov, Connections betweem some properties of n-group rings and group rings (Russian), Math. Montisnigri 11 (1999), 151-158.

Received 1 July 2002
Revised 20 February 2003